VARIABLE BESOV AND TRIEBEL-LIZORKIN SPACES

By Jingshi Xu. 2008

120 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/99dfe102d80c378c3291b1ffe2bc7db928b90556

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

1. Dachun Yang
2. H. Kempka
3. Kwok-Pun Ho
4. Ciqiang Zhuo
5. Jan Vyb'iral
6. Alexandre Almeida
7. P. Hasto
8. Jingshi Xu

Citations in the corpus

• ATOMIC DECOMPOSITION OF HARDY-MORREY SPACES WITH VARIABLE EXPONENTS (2015, methodology): “On the other hand, it gives an extension of the variable Triebel–Lizorkin spaces considered in [18, 61, 62] to the Morrey spaces setting.”
• Function spaces of variable smoothness and integrability (2007, background): “Hardy spaces have thus far not 1After the completion of this paper we learned that Xu [56, 57] has studied Besov and Triebel–Lizorkin spaces with variablep, but fixesq andα.”
• Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “Along a different line of study, Xu [66, 67] studied Besov spaces B p(·),q(R ) and Triebel-Lizorkin spaces F s p(·),q(R ) with variable exponent p(·) but fixed q and s.”
• Variable weak Hardy spaces and their applications (2016, background): “On the other hand, based on the variable Lebesgue space, several variable function spaces are developed rapidly in recent years (see, for example, [3, 4, 12, 14, 32, 41, 44, 45]).”
• An atomic decomposition of variable Besov and Triebel-Lizorkin spaces (2009, methodology): “Inspired by the mentioned references, similar to classical Besov and Triebel-Lizorkin spaces, the author introduced the variable Besov spaces and Triebel-Lizorkin spaces in [27].”
• SOBOLEV AND JAWERTH EMBEDDINGS FOR SPACES WITH VARIABLE SMOOTHNESS AND INTEGRABILITY (2009, background): “or convergent at infinity. We refer at least to [23] and [ 39 ].”
• Vector-valued singular integral operators on Morrey type spaces and variable Triebel-Lizorkin-Morrey spaces (2012, methodology): “For the rest of this paper, we use the lifting principle to introduce and study some new Morrey type spaces related to several Banach function spaces appeared in [4, 5, 20, 24, 25, 26, 32, 35, 41, 42, 43, 44, 47, 52, 56, 66, 67, 71, 73, 74, 75].”
• Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, methodology): “Taking s ∈ R and q ∈ (0,∞] as constants we derive the spaces F s p(·),q(R n) and Bs p(·),q(R n) studied by Xu in [61] and [62].”
• The relation between variable Bessel potential spaces and Triebel–Lizorkin spaces (2008, methodology): “Inspired by the mentioned references, similar to classical Besov and Triebel–Lizorkin spaces, the author introduced the variable Besov spaces and Triebel–Lizorkin spaces in 13 .”
• Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “For more developments of function spaces with variable exponents, we refer the reader to [6, 26, 44, 57, 58, 75, 76, 77, 78, 82] and their references.”
• Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, background): “Later, Xu [73, 74, 75] studied Besov spaces B p(·),q(R ) and Triebel-Lizorkin spaces F s p(·),q(R ) with the variable exponent p(·) but invariable exponents q and s.”
• A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces (2012, unknown): “Another direction is pursued via replacing the space Lp(Rn) by the Morrey space Mu(R); see [48, 52, 53], or generalizations thereof [43, 80, 82, 89, 95, 96, 98, 99, 104].”
• Besov spaces with variable smoothness and integrability (2010, background): “There was taken a step further by Xu [44, 45, 46], who considered Besov B p(·), q and Triebel–Lizorkin F α p(·), q spaces with variable p, but fixed q and α.”
• 2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability (2009, methodology): “For variable p ∈ P(R) and wj(x) = 2 the spaces considered by Xu in [37] are contained in the above scale.”