Hardy spaces with variable exponents and generalized Campanato spaces
Eiichi Nakai,Yoshihiro Sawano +1 more
TLDR
In this paper, the authors define Hardy spaces with variable exponents on R n by the grand maximal function, and then investigate their several properties, including the atomic decomposition and the molecular decomposition.About:
This article is published in Journal of Functional Analysis.The article was published on 2012-05-01 and is currently open access. It has received 325 citations till now. The article focuses on the topics: Hardy space & Interpolation space.read more
Citations
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Function spaces of variable smoothness and integrability
TL;DR: In this paper, the authors introduce Triebel-Lizorkin spaces with variable smoothness and integrability, and show that these spaces are well-defined independent of the choice of basis functions.
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New Hardy Spaces of Musielak–Orlicz Type and Boundedness of Sublinear Operators
TL;DR: In this article, a new class of Hardy spaces, called Hardy spaces of Musielak-Orlicz type, was introduced, which generalize the Hardy space of Janson, Garcia-Cuerva, Stromberg and Torchinsky.
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Variable Hardy spaces
David Cruz-Uribe,Daniel Wang +1 more
TL;DR: In this article, the theory of variable exponent Hardy spaces Hp(·) was developed, and the authors gave equivalent definitions in terms of maximal operators that are analogous to the classical theory.
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Atomic Decompositions of Hardy Spaces with Variable Exponents and its Application to Bounded Linear Operators
TL;DR: In this article, the authors prove the boundedness of commutators and fractional integral operators as well as the Hardy operators based on the atomic decomposition of Hardy spaces with variable exponents.
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New Hardy spaces of Musielak-Orlicz type and boundedness of sublinear operators
TL;DR: In this paper, a new class of Hardy spaces, called Hardy spaces of Musielak-Orlicz type (H^{\varphi(cdot,\cdot)}(\mathbb R^n)$, were introduced, which generalize the Hardy-Orliquez spaces of Janson and the weighted Hardy spaces.
References
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Book
Harmonic Analysis: Real-variable Methods, Orthogonality, and Oscillatory Integrals
Elias M. Stein,Timothy S Murphy +1 more
TL;DR: In this article, the authors introduce the Heisenberg group and describe the Maximal Operators and Maximal Averages and Oscillatory Integral Integrals of the First and Second Kind.
Book
Theory of function spaces
TL;DR: In this article, the authors measure smoothness using Atoms and Pointwise Multipliers, Wavelets, Spaces on Lipschitz Domains, Wavelet and Sampling Numbers.
Journal ArticleDOI
H p spaces of several variables
Book
Classical Fourier Analysis
TL;DR: In this paper, the Fourier Transform and Distributions of convolutional neural networks have been studied in the context of Trigonometric Identities and Inequalities and Mean Value Theorem in Variables.
Book
Weighted norm inequalities and related topics
TL;DR: Theories de la factorisation and inegalites en norme ponderees of Hardy as mentioned in this paper have been studied in the context of factorization, and a variable reelle des espaces de Hardy has been proposed.