Remarks on Almost Everywhere Convergence and Approximate Identities  

作　　者：Sean Douglas Loukas Grafakos 

机构地区：[1]Department of Mathematics,University of Missouri,Columbia MO 65211,USA

出　　处：《Acta Mathematica Sinica,English Series》2025年第1期255-272,共18页数学学报(英文版)

基　　金：the support of the University of Missouri Research Council;the support of the Simons Foundation under Grant 624733。

摘　　要：We prove almost everywhere convergence for convolutions of locally integrable functions with shrinking L^(1) dilations of a fixed integrable kernel with an integrable radially decreasing majorant.The set on which the convergence holds is an explicit subset of the Lebesgue set of the locally integrable function of full measure.This result can be viewed as an extension of the Lebesgue differentiation theorem in which the characteristic function of the unit ball is replaced by a more general kernel.We obtain a similar result for multilinear convolutions.

关 键 词：Almost everywhere convergence approximate identities Lebesgue set 

分 类 号：O15[理学—数学]