Characterization of the variable exponent Bessel potential spaces via the Poisson semigroup

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:365

Article

Rafeiro, Humberto¹  Samko, Stefan¹ 

[1] Univ Algarve, Fac Ciencias & Tecnol, P-8000117 Faro, Portugal

关键词: Riesz fractional derivative;    Riesz potential operator;    Bessel potential space;    Hypersingular integral;    Grunwald-Letnikov approach;   

DOI  :  10.1016/j.jmaa.2009.11.008

来源: Elsevier

【 摘 要 】

Under the standard assumptions on the variable exponent p(x) (log- and decay conditions), we give a characterization of the variable exponent Bessel potential space B-alpha[Lp(-)(R-n)] in terms of the rate of convergence of the Poisson semigroup P-t. We show that the existence of the Riesz fractional derivative D-alpha f in the space Lp(-)(R-n) is equivalent to the existence of the limit 1/epsilon(alpha)(I - P-epsilon)(alpha) f. In the pre-limiting case sup(x) p(x) < n/alpha we show that the Bessel potential space is characterized by the condition parallel to(I - P-epsilon)(alpha) f parallel to p((.)) <= C epsilon(alpha). (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free