Equivalent Normings of Spaces of Functions of Variable Smoothness

By O. V. Besov. 2003

47 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7d4f8fa018a923036eb27f3f9e83680f03f2b508

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1. Dachun Yang
2. Ciqiang Zhuo
3. Wen Yuan
4. H. Kempka
5. Jan Vyb'iral
6. Alexandre Almeida
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8. Jun Liu

Citations in the corpus

• Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, background): “A similar characterization for Fwp(·),q(·)(Rn) and details how these functions k0, k ∈ S(Rn) can be constructed can be found in [30].”
• Function spaces of variable smoothness and integrability (2007, background): “Function spaces of variable smoothness have recently been studied by Besov [5, 6, 7, 8].”
• 2-Microlocal Besov and Triebel-Lizorkin Spaces of Variable Integrability (2009, methodology): “1 in [3] for the case of the usual distributions (w(x) = ln(1 + |x|) in the notation of Besov).”
• Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “When Leopold [33, 34, 35, 36] and Leopold and Schrohe [37] studied pseudo-differential operators, they introduced related Besov spaces with variable smoothness, B s(·) p,p (R), which were further generalized to the case that q 6= p, including Bs(·) p,q (R) and F s(·) p,q (R), by Besov [4, 5, 6].”
• Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, methodology): “Function spaces of variable smoothness including Besov space B s(·) p,q (R) and Triebel-Lizorkin space F s(·) p,q (R) have been studied by Besov [7, 8, 9], which was a generalization of Leopold’s work.”
• Atomic, molecular and wavelet decomposition of 2-microlocal Besov and Triebel-Lizorkin spaces with variable integrability (2010, background): “Restricted to the usual distributions, our approach is more general because negative smoothness is allowed (α1, α2 ∈ R in contrast to 0 6 α1 6 α2 in [6]).”
• Besov spaces with variable smoothness and integrability (2010, background): “Function spaces of variable smoothness have recently been studied by Besov [8, 9, 10]: he generalized Leopold’s work by considering both Triebel– Lizorkin spaces F α(·) p, q and Besov spaces B α(·) p, q in R.”