Showing papers on "Birnbaum–Orlicz space published in 2015"
Book•
07 Apr 2015
TL;DR: In this article, the fixed point theory in metric spaces is introduced and fixed point construction processes are described. And fixed point existence theorem in modular function spaces is discussed in detail.
Abstract: Introduction.- Fixed Point Theory in Metric Spaces: An Introduction.- Modular Function Spaces.- Geometry of Modular Function Spaces.- Fixed Point Existence Theorems in Modular Function Spaces.- Fixed Point Construction Processes.- Semigroups of Nonlinear Mappings in Modular Function Spaces.- Modular Metric Spaces.
196 citations
Book•
13 May 2015TL;DR: The Spaces Hs and Second-Order Strongly Elliptic Systems in Lipschitz Domains as mentioned in this paper are a generalization of the spaces Hs used in the space Hs.
Abstract: Preface.- Preliminaries.- 1 The Spaces Hs..- 2 Elliptic Equations and Elliptic Boundary Value Problems.- 3 The Spaces Hs and Second-Order Strongly Elliptic Systems in Lipschitz Domains.- 4 More General Spaces and Their Applications.- References.- Index.
118 citations
TL;DR: In this paper, a sufficient condition for the boundedness of the maximal operator on generalized Orlicz spaces is presented. But this condition is not applicable to the double phase functional and does not cover the case of variable exponent Lebesgue spaces.
98 citations
01 Jan 2015
TL;DR: In this paper, the bounds of linear operators defined on Hp(X) are defined for regular quasi-metric spaces, and the Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces.
Abstract: Introduction. - Geometry of Quasi-Metric Spaces.- Analysis on Spaces of Homogeneous Type.- Maximal Theory of Hardy Spaces.- Atomic Theory of Hardy Spaces.- Molecular and Ionic Theory of Hardy Spaces.- Further Results.- Boundedness of Linear Operators Defined on Hp(X).- Besov and Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces.
63 citations
TL;DR: In this paper, the authors considered the split common null point problem in Banach spaces and proved a strong convergence theorem for finding a solution of the problem in the Banach space.
Abstract: In this paper, we consider the split common null point problem in Banach spaces. Then using the metric resolvents of maximal monotone operators and the metric projections, we prove a strong convergence theorem for finding a solution of the split common null point problem in Banach spaces. The result of this paper seems to be the first one to study it outside Hilbert spaces.
56 citations
TL;DR: In this paper, the problem of the order of approximation for the nonlinear multivariate sampling Kantorovich operators is investigated for the case of uniformly continuous and bounded functions belonging to Lipschitz classes and functions in Orlicz spaces.
Abstract: In this article, the problem of the order of approximation for the nonlinear multivariate sampling Kantorovich operators is investigated. The case of uniformly continuous and bounded functions belonging to Lipschitz classes is considered, as well as the case of functions in Orlicz spaces. In the latter setting, suitable Zygmung-type classes are introduced by using the modular functionals of the spaces. The results obtained show that the order of approximation depends on both the kernels of our operators and the engaged functions. Several examples of kernels are considered in special instances of Orlicz spaces, typically used in approximation theory and for applications to signal and image processing.
54 citations
TL;DR: Differences between these two generalized Orlicz-Morrey spaces are investigated in some typical cases and property of the characteristic function of the Cantor set is investigated.
44 citations
TL;DR: In this article, it was shown that the characteristic function of the half-space is a pointwise multiplier on Besselpotential spaces with values in a UMD Banach space.
Abstract: We investigate pointwise multipliers on vector-valued function spaces over \({\mathbb {R}}^d\), equipped with Muckenhoupt weights. The main result is that in the natural parameter range, the characteristic function of the half-space is a pointwise multiplier on Bessel-potential spaces with values in a UMD Banach space. This is proved for a class of power weights, including the unweighted case, and extends the classical result of Shamir and Strichartz. The multiplication estimate is based on the paraproduct technique and a randomized Littlewood–Paley decomposition. An analogous result is obtained for Besov and Triebel–Lizorkin spaces.
40 citations
TL;DR: In this paper, the authors compare B-p,q(0,b+1/2) = B-2,2( 0,b) for b > 1/2.
38 citations
Book•
01 Jan 2015
TL;DR: In this article, the Dirichlet Principle is used to describe the Diriclet principle of singular integral operators and Vector-Valued Inequalities (VINI) of the Lp-multipliers and function spaces.
Abstract: 13 Maximal Function Bounding Averages and Pointwise Convergence 14 Harmonic-Hardy Spaces hp(H) 15 Sobolev Spaces A Resolution of the Dirichlet Principle 16 Singular Integral Operators and Vector-Valued Inequalities 17 Littlewood-Paley Theory, Lp-Multipliers and Function Spaces 18 Morrey and Campanato vs Hardy and John-Nirenberg Spaces 19 Layered Potentials, Jump Relations and Existence Theorems 20 Second Order Equations in Divergence Form: Continuous Coefficients 21 Second Order Equations in Divergence Form: Measurable Coefficients A Partition of Unity B Total Boundedness and Compact Subsets of Lp C Gamma and Beta Functions D Volume of the Unit n-Ball E Integrals Related to Abel and Gauss Kernels F Hausdorff Measures Hs G Evaluation of Some Integrals Over H Sobolev Spaces
TL;DR: The reiteration formula and limiting interpolation are applied to investigate several problems on Besov spaces, including embeddings in Lorentz-Zygmund spaces and distribution of Fourier coefficients.
TL;DR: In this article, a new class of rearrangement-invariant Banach function spaces, independent of the variable Lebesgue spaces, whose function norm is ρ ( f ) = ess sup x ∈ ( 0, 1 ) ρ p( x ) ( δ ( x ) f ( ⋅ ) ) is constructed.
TL;DR: In this paper, the authors established a Bloch-type growth theorem for generalized Bloch type spaces and discussed relationships between Dirichlet-type spaces and Hardy-type space on certain classes of complex-valued functions.
Abstract: In this paper, we establish a Bloch-type growth theorem for generalized Bloch-type spaces and discuss relationships between Dirichlet-type spaces and Hardy-type spaces on certain classes of complex-valued functions. Then we present some applications to non-homogeneous Yukawa PDEs. We also consider some properties of the Lipschitz-type spaces on certain classes of complex-valued functions. Finally, we will study a class of composition operators on these spaces.
TL;DR: In this paper, the authors studied the Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and the Dirichlet space, which is a Hilbert space.
Abstract: In this paper we begin the study of some important Banach spaces of slice hyperholomorphic functions, namely the Bloch, Besov and weighted Bergman spaces, and we also consider the Dirichlet space, which is a Hilbert space. The importance of these spaces is well known, and thus their study in the framework of slice hyperholomorphic functions is relevant, especially in view of the fact that this class of functions has recently found several applications in operator theory and in Schur analysis. We also discuss the property of invariance of these function spaces with respect to Mobius maps by using a suitable notion of composition.
TL;DR: In this paper, the authors generalize Uspenskiĭ's results and prove the optimality of these generalizations, and show how classical results on the functional calculus in the Besov spaces can be obtained as straightforward consequences of the theory of weighted Sobolev spaces.
Abstract: We give short simple proofs of Uspenskiĭ’s results characterizing Besov spaces as trace spaces of weighted Sobolev spaces. We generalize Uspenskiĭ’s results and prove the optimality of these generalizations. We next show how classical results on the functional calculus in the Besov spaces can be obtained as straightforward consequences of the theory of weighted Sobolev spaces.
TL;DR: For systems of linear differential equations of order r ∈ ℕ, this paper studied the most general class of inhomogeneous boundary-value problems whose solutions belong to the Sobolev space and showed that these problems are Fredholm problems and established the conditions under which these problems have unique solutions continuous with respect to the parameter in the norm of this space.
Abstract: For systems of linear differential equations of order r ∈ ℕ, we study the most general class of inhomogeneous boundary-value problems whose solutions belong to the Sobolev space W
+
([a, b],ℂ
m
), where m, n + 1 ∈ ℕ and p ∈ [1,∞). We show that these problems are Fredholm problems and establish the conditions under which these problems have unique solutions continuous with respect to the parameter in the norm of this Sobolev space.
Book•
25 Jun 2015
TL;DR: In this paper, the bounds of linear operators defined on Hp(X) are defined for regular quasi-metric spaces, and the Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces.
Abstract: Introduction. - Geometry of Quasi-Metric Spaces.- Analysis on Spaces of Homogeneous Type.- Maximal Theory of Hardy Spaces.- Atomic Theory of Hardy Spaces.- Molecular and Ionic Theory of Hardy Spaces.- Further Results.- Boundedness of Linear Operators Defined on Hp(X).- Besov and Triebel-Lizorkin Spaces on Ahlfors-Regular Quasi-Metric Spaces.
TL;DR: In this article, a generalization of Sobolev's inequality for Soboleve functions in Musielak-Orlicz-Hajlasz-Sobolev spaces is presented.
Abstract: Our aim in this paper is to study Musielak-Orlicz-Sobolev spaces on metric measure spaces. We consider a Hajlasz-type condition and a Newtonian condition. We prove that Lipschitz continuous functions are dense, as well as other basic properties. We study the relationship between these spaces, and discuss the Lebesgue point theorem in these spaces. We also deal with the boundedness of the Hardy-Littlewood maximal operator on Musielak-Orlicz spaces. As an application of the boundedness of the Hardy-Littlewood maximal operator, we establish a generalization of Sobolev’s inequality for Sobolev functions in Musielak-Orlicz-Hajlasz-Sobolev spaces.
01 Mar 2015
TL;DR: In this paper, the authors introduce Besov-type spaces with variable smoothness and integrability, which unify and generalize the Besov type spaces with fixed exponents.
Abstract: In this article we introduce Besov-type spaces with variable smoothness and integrability, which unify and generalize the Besov-type spaces with fixed exponents. Under natural regularity assumptions on the exponent functions, we show that our spaces are well-defined, i.e., independent of the choice of basis functions and we establish some properties of these function spaces. Moreover the Sobolev embeddings for these function spaces are obtained.
TL;DR: In this paper, a class of linear-quadratic infinite horizon optimal control problems is considered and a Pontryagin type Maximum Principle is established as a necessary optimality condition including transversality conditions.
Abstract: In this paper a class of linear-quadratic infinite horizon optimal control problems is considered. Problems of this type are not only of practical interest. They also appear as an approximation of nonlinear problems. The key idea is to introduce weighted Sobolev spaces as state space and weighted Lebesgue spaces as control spaces into the problem setting. We investigate the question of existence of an optimal solution in these spaces and establish a Pontryagin type Maximum Principle as a necessary optimality condition including transversality conditions.
Posted Content•
TL;DR: The concept of profile decompositions was introduced in this article to formalize concentration compactness arguments on the functional-analytic level, providing a powerful refinement of the Banach-Alaoglu weak-star compactness theorem.
Abstract: The concept of a profile decomposition formalizes concentration compactness arguments on the functional-analytic level, providing a powerful refinement of the Banach-Alaoglu weak-star compactness theorem. We prove existence of profile decompositions for general bounded sequences in uniformly convex Banach spaces equipped with a group of bijective isometries, thus generalizing analogous results previously obtained for Sobolev spaces and for Hilbert spaces. Profile decompositions in uniformly convex Banach spaces are based on the notion of $\Delta$-convergence by T. C. Lim instead of weak convergence, and the two modes coincide if and only if the norm satisfies the well-known Opial condition, in particular, in Hilbert spaces and $\ell^{p}$-spaces, but not in $L^{p}(\mathbb R^{N})$, $p
eq2$. $\Delta$-convergence appears naturally in the context of fixed point theory for non-expansive maps. The paper also studies connection of $\Delta$-convergence with Brezis-Lieb Lemma and gives a version of the latter without an assumption of convergence a.e.
TL;DR: In this article, the optimal domain and optimal range point of view of the Cesaro spaces are investigated from an optimal domain perspective. But there is a big difference between the cases on [0, ∞) and on [ 0, 1], as we can see in Theorem 1.
Abstract: Cesaro spaces are investigated from the optimal domain and optimal range point of view. There is a big difference between the cases on [0, ∞) and on [0, 1], as we can see in Theorem 1. Moreover, we present an improvement of Hardy’s inequality on [0, 1] which plays an important role in these considerations.
TL;DR: In this article, the authors introduce and study some generalized paranormed sequence spaces defined by Musielak-Orlicz functions as well as by a sequence of modulus functions.
Abstract: In the present paper we introduce and study some generalized paranormed sequence spaces defined by Musielak-Orlicz functions as well as by a sequence of modulus functions. We also study some topological properties and prove some inclusion relations between these spaces.
Posted Content•
TL;DR: In this article, the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval is studied and it is shown that the warped products of the metric measure spaces possess the Soboleve-to-Lipschitz property.
Abstract: We study the structure of Sobolev spaces on the cartesian/warped products of a given metric measure space and an interval.
Our main results are:
- the characterization of the Sobolev spaces in such products
- the proof that, under natural assumptions, the warped products possess the Sobolev-to-Lipschitz property, which is key for geometric applications.
The results of this paper have been needed in the recent proof of the `volume-cone-to-metric-cone' property of ${\sf RCD}$ spaces obtained by the first author and De Philippis.
TL;DR: In this paper, the boundedness of the Hardy-Littlewood maximal operator on Herz-Morrey spaces was studied and Sobolev's inequalities for Riesz potentials of functions were established.
Abstract: Our aim in this paper is to deal with the boundedness of the Hardy–Littlewood maximal operator on Herz–Morrey spaces and to establish Sobolev’s inequalities for Riesz potentials of functions in Herz–Morrey spaces Further, we discuss the associate spaces among Herz–Morrey spaces
TL;DR: In this article, it was shown that multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal.
Abstract: We continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with restrictions of a universal space, namely the Drury-Arveson space. Instead, we work directly with the Hilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study of a special class of Nevanlinna-Pick spaces on homogeneous varieties. We provide a complete answer to the question of when two multiplier algebras of spaces of this type are algebraically or isometrically isomorphic. This generalizes results of Davidson, Ramsey, Shalit, and the author.
TL;DR: In this article, the boundedness and compactness of a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces are investigated, and the authors show that the compactness is bounded.
Abstract: The boundedness and compactness of a product-type operator from Zygmund-type spaces to Bloch-Orlicz spaces are investigated in this paper.
TL;DR: In this article, it was shown that among all Musielak-Orlicz function spaces on a σ-finite non-atomic complete measure space equipped with either the Luxemburg norm or the Orlicz norm, the only spaces with the Daugavet property are L 1, L ∞, L 1 ⊕ 1 L ǫ ∞ ∞ and L 1 ∞ l ∞.