Vol. 69, No. 2, 1977

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Summability Rr for double series

Marvin J. Kohn

Vol. 69 (1977), No. 2, 433–448

Let r be a positive integer. A trigonometric series T of a single variable is said to be summable Rr 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 Rr has been applied to double trigonometric series. We study here summability Rr, for odd values of r, for double trigonometric series. We obtain a connection between Bochner-Riesz summable series and series which are summable Rr.

Mathematical Subject Classification
Primary: 42A92, 42A92
Received: 30 March 1976
Revised: 6 October 1976
Published: 1 April 1977
Marvin J. Kohn