Convergence of iterates of convolution operators in LP spaces

被引：6
|
作者：
Mustafayev, Heybetkulu [1 ]
机构：
[1] Van Yuzuncu Yil Univ, Fac Sci, Dept Math, Van, Turkey
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2019年 / 152卷
关键词：
Locally compact abelian group; Group algebra; Measure algebra; L-P-space; Convolution operator; Convergence; ERGODIC-THEOREMS; BANACH-ALGEBRAS; MULTIPLIERS;
D O I：
10.1016/j.bulsci.2019.01.005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a locally compact abelian group and let M (G) be the measure algebra of G. Assume that mu is an element of M (G) is power bounded, that is, sup(n >= 0) parallel to mu(n)parallel to(1) < infinity. This paper is concerned mainly with finding necessary and sufficient conditions for strong convergence of iterates of the convolution operators T(mu)f : = mu * f in L-P (G) (1 <= p < infinity) spaces. Some related problems are also discussed. (C) 2019 Elsevier Masson SAS. All rights reserved.
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页码：61 / 92
页数：32
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