Convergence of iterates of convolution operators in L-P spaces


Mustafayev H.

BULLETIN DES SCIENCES MATHEMATIQUES, cilt.152, ss.61-92, 2019 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 152
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1016/j.bulsci.2019.01.005
  • Dergi Adı: BULLETIN DES SCIENCES MATHEMATIQUES
  • Sayfa Sayıları: ss.61-92

Özet

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.