Besov spaces with variable smoothness and integrability

By Alexandre Almeida, P. Hasto. 2010

223 citations recorded by the source corpus.

Abstract In this article we introduce Besov spaces with variable smoothness and integrability indices. We prove independence of the choice of basis functions, as well as several other basic properties. We also give Sobolev-type embeddings, and show that our scale contains variable order Holder–Zygmund spaces as special cases. We provide an alternative characterization of the Besov space using approximations by analytic functions.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/a84dc458c158e67b4cb8b90b6b61912b42958d6e

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In Applied Mathematics

1. Dachun Yang
2. Wen Yuan
3. Ciqiang Zhuo
4. Jun Liu
5. Xianjie Yan
6. Yong Jiao
7. Dejian Zhou
8. Jan Vyb'iral

In Mathematical Physics

1. Dachun Yang
2. Wen Yuan
3. Ciqiang Zhuo
4. Jun Liu
5. Xianjie Yan
6. Jan Vyb'iral
7. H. Kempka
8. Kwok-Pun Ho

Citations in the corpus

• Besov-Type Spaces with Variable Smoothness and Integrability (2015, background): “2. (i) If φ(Q) = 1 for all cubes Qof Rn, then Bs(·),φ p(·),q(·)(R n) = Bs(·) p(·),q(·)(R n),where Bs(·) p(·),q(·)(R n) denotes the Besov space with variable smoothness and integrability introduced in [3]. (ii) If p, q, sare constant exponents and φ(Q) := |Q|τ with τ∈ [0,∞) for all cubes Qof Rn, then”
• Lorentz spaces with variable exponents (2012, methodology): “It was shown in [1] that it always constitutes a quasi-norm if p, q > 0.”
• Anisotropic Variable Hardy-Lorentz Spaces and Their Real Interpolation (2017, background): “awano [66], Zhuo et al. [85] and Yang et al. [81] further completed the theory of these variable Hardy spaces. 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. In particular, Kempka and Vyb´ıral [44”
• Martingale Hardy spaces with variable exponents (2014, background): “We also note that in the recent years more attention was turned to the study of function spaces with variable exponent in harmonic analysis; see for instance [3, 6, 7, 10, 22, 25].”
• 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]).”
• A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces (2012, unknown): “29)], we see that, for all t ∈ [1, 2], N ≫ 1, r ∈ (0,∞), l ∈ N and x ∈ Rn [ (φ2−ltf)a(x) ]r .”
• Spaces of Variable Smoothness and Integrability: Characterizations by Local Means and Ball Means of Differences (2011, methodology): “We recall the definition of the spaces Bs(·) p(·),q(·)(Rn) and F s(·) p(·),q(·)(Rn), as given in [16] and [1].”
• 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].”
• Triebel-Lizorkin-Type Spaces with Variable Exponents (2015, background): “(·),q(R n) with the only index qbeing a constant, which is a quite natural case, since the norm in the Besov space is usually defined via the iterated space ℓq(Lp(Rn)). Furthermore, Almeida and H¨asto [4] introduced and investigated the Besov space Bs(·) p(·),q(·)(R n) with all three variable exponen”