Some Tauberian Theorems for Cesaro Summability of Double Integrals over R-+(2)


Findik G., ÇANAK İ.

FILOMAT, vol.35, no.15, pp.5279-5291, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 15
  • Publication Date: 2021
  • Doi Number: 10.2298/fil2115279f
  • Title of Journal : FILOMAT
  • Page Numbers: pp.5279-5291
  • Keywords: one-sided and two-sided Tauberian conditions, improper double integrals, Cesaro summability (C, 1, 1), (C, 1, 0) and (C, 0, 1), convergence in Pringsheim's sense, slow decrease and strong slow decrease in different senses, slow oscillation and strong slow oscillation in different senses

Abstract

In this paper, we obtain one-sided and two-sided Tauberian conditions of Landau and Hardy types for (C, 1, 0) and (C, 0,1) summability methods for improper double integrals under which convergence of improper double integrals follows from (C, 1, 0) and (C, 0,1) summability of improper double integrals. We give similar results for (C, 1,1) summability method of improper double integrals. In general, we obtain Tauberian conditions in terms of the concepts of slowly decreasing (resp. oscillating) and strong slowly decreasing (resp. oscillating) functions in different senses for Cesaro summability methods of real or complex-valued locally integrable functions on [0, infinity) x [0, infinity) in different senses.