Convergence of iterates of convolution operators in L-P spaces

Mustafayev, Heybetkulu

doi:10.1016/j.bulsci.2019.01.005

Convergence of iterates of convolution operators in L-P spaces

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Mustafayev H.

BULLETIN DES SCIENCES MATHEMATIQUES, vol.152, pp.61-92, 2019 (SCI-Expanded)

Publication Type: Article / Article
Volume: 152
Publication Date: 2019
Doi Number: 10.1016/j.bulsci.2019.01.005
Journal Name: BULLETIN DES SCIENCES MATHEMATIQUES
Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
Page Numbers: pp.61-92
Van Yüzüncü Yıl University Affiliated: Yes

Abstract

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.