Characterizations of Besov and Triebel Lizorkin spaces via averages on balls

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:433

Article

Dai, Feng¹  Gogatishvili, Amiran²  Yang, Dachun³  Yuan, Wen³ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

[2] Acad Sci Czech Republ, Inst Math, CR-11567 Prague 1, Czech Republic

[3] Beijing Normal Univ, Sch Math Sci, Minist Educ, Lab Math & Complex Syst, Beijing 100875, Peoples R China

关键词: Besov space;    Triebel-Lizorkin space;    Average on ball;    Difference;    Calderon reproducing formula;   

DOI  :  10.1016/j.jmaa.2015.08.054

来源: Elsevier

【 摘 要 】

Let l is an element of N and p is an element of E (1, infinity]. In this article, the authors prove that the sequence {f - B-l,B-2-k, f}k is an element of z consisting of the differences between f and the ball average Be,2-k f characterizes the Besov space Eq (lRn) with q E (0,00] and the Triebel-Lizorkin space F-p,q(alpha)(R-n) with q is an element of(1, infinity] when the smoothness order alpha is an element of(0, 2l). More precisely, it is proved that f - B-l,B-2-k f plays the same role as the approximation to the identity phi(2-k) * f appearing in the definitions of B-p,q(alpha) (R-n) and F-p,g(alpha) (R-n). The corresponding results for inhomogeneous Besov and Triebel-Lizorkin spaces are also obtained. These results, for the first time, give a way to introduce Besov and TriebelLizorkin spaces with any smoothness order in (0, 2l) on spaces of homogeneous type, where l is an element of N. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

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