Bessel capacities and rectangular differentiation in Besov spaces

[摘要] We consider the differentiation of integrals of functions in Besov spaces with respect to the basis of arbitrarily oriented rectangular parallelepipeds in R-n. We study almost everywhere convergence with respect to Bessel capacities. These outer measures are more sensitive than n-dimensional Lebesgue measure, and therefore we improve the positive results in [H. Aimar, L. Forzani, V. Naibo, Rectangular differentiation of integrals of Besov functions, Math. Res. Lett. 9 (2-3) (2002) 173-189]. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] differentiation;Besov spaces;maximal functions;Bessel capacities