Mixed means over balls and annuli and lower bounds for operator norms of maximal functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:291

Article

Cizmesija, A ; Peric, I

关键词: mixed means;    integral means;    balls and annuli;    power weights;    Hardy's inequality;    Hardy-Littlewood maximal function;    spherical maximal function;   

DOI  :  10.1016/j.jmaa.2003.11.018

来源: Elsevier

【 摘 要 】

In this paper we prove mixed-means inequalities for integral power means of an arbitrary real order, where one of the means is taken over the ball B(x, delta\x\), centered at X is an element of R-n and of radius delta\x\, delta > 0. Therefrom we deduce the corresponding Hardy-type inequality, that is, the operator norm of the operator S-delta which averages if \f\ is an element of L-p (R-n) over B(x, delta\x\), introduced by Christ and Grafakos in Proc. Amer. Math. Soc. 123 (1995) 1687-1693. We also obtain the operator norm of the related limiting geometric mean operator, that is, Carleman or Levin-Cochran-Lee-type inequality. Moreover, we indicate analogous results for annuli and discuss estimations related to the Hardy-Littlewood and spherical maximal functions. (C) 2003 Elsevier Inc. All rights reserved.

【 授权许可】

Free