On Embeddings of Logarithmic Bessel Potential Spaces
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TLDR
In this paper, the role of the logarithmic terms involved in the norms of the space mentioned is clarified and refinements of the Sobolev embedding theorems, Trudinger's limiting embedding as well as embeddings of Soboleve spaces into space of λ-Holder continuous functions are presented.About:
This article is published in Journal of Functional Analysis.The article was published on 1997-05-01 and is currently open access. It has received 75 citations till now. The article focuses on the topics: Interpolation space & Sobolev inequality.read more
Citations
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Journal ArticleDOI
Characterisations of function spaces of generalised smoothness
Walter Farkas,Hans-Gerd Leopold +1 more
TL;DR: In this paper, the authors investigate function spaces of generalised smoothness of Besov and Triebel-Lizorkin type and derive equivalent quasi-norms in terms of maximal functions and local means.
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On generalized Lorentz-Zygmund spaces
Bohumír Opic,Luboš Pick +1 more
TL;DR: In this article, necessary and sufficient conditions for a generalized Lorentz-Zygmund space to be a Banach function space and to have absolutely continuous (quasi-)norm are established.
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Sobolev embeddings into BMO, VMO, and L∞
Andrea Cianchi,Luboš Pick +1 more
TL;DR: In this paper, the Sobolev space of functions whose gradient belongs to a function is defined as a rearrangement-invariant Banach function space, and necessary and sufficient conditions on the conditions under which a function from a function X is continuously embedded into BMO or into L�Ωℓℚ ℓ ∞∞.
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Limiting reiteration for real interpolation with slowly varying functions
TL;DR: In this paper, the authors present reiteration formulae with limiting values θ = 0 and θ= 1 for a real interpolation method involving slowly varying functions, which yield improvements of limiting Sobolev-type embeddings due to Trudinger, Hansson, Brezis and Wainger.
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Strong and Weak Type Inequalities for Some Classical Operators in Orlicz Spaces
TL;DR: In this article, a characterization of Young functions A and B having the property that the Hardy-Littlewood maximal operator or the Hilbert and Riesz transforms are of weak or strong type from the Orlicz space LA into itself is given.
References
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Book
Singular Integrals and Differentiability Properties of Functions.
TL;DR: Stein's seminal work Real Analysis as mentioned in this paper is considered the most influential mathematics text in the last thirty-five years and has been widely used as a reference for many applications in the field of analysis.
Book
Graduate Texts in Mathematics
Rajendra Bhatia,Glen Bredon,Wolfgang Walter,Joseph J. Rotman,M. Ram Murty,Jane Gilman,Peter Walters,Martin Golubitsky,Ioannis Karatzas,Henri Cohen,Raoul Bott,Gaisi Takeuti,Béla Bollobás,John M. Lee,Jiří Matoušek,Saunders Mac Lane,John L. Kelley,B. A. Dubrovin,Tom M. Apostol,John Stillwell,William Arveson +20 more
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On Imbeddings into Orlicz Spaces and Some Applications
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A note on limiting cases of sobolev embeddings and convolution inequalities
Haim Brezis,Stephen Wainger +1 more
TL;DR: In this paper, a note on limiting cases of sobolev embeddings and convolution inequalities is given, along with a discussion of the relation between the two types of embedding.