Summability R_r for double series

Marvin J. Kohn

Vol. 69 (1977), No. 2, 433–448

DOI: 10.2140/pjm.1977.69.433

Abstract

Let r be a positive integer. A trigonometric series T of a single variable is said to be summable R_r at 𝜃₀ if the series obtained by r times formally integrating T has an r-th symmetric derivative at 𝜃₀. For even values of r, summability R_r has been applied to double trigonometric series. We study here summability R_r, for odd values of r, for double trigonometric series. We obtain a connection between Bochner-Riesz summable series and series which are summable R_r.

Mathematical Subject Classification

Primary: 42A92, 42A92

Milestones

Received: 30 March 1976

Revised: 6 October 1976

Published: 1 April 1977