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HARMONIC AND LOGARITHMIC SUMMABILITY OF ORTHOGONAL SERIES ARE EQUIVALENT UP TO A SET OF MEASURE ZERO

Published online by Cambridge University Press:  01 February 1999

F. MÓRICZ  and
U. STADTMÜLLER
F. MÓRICZ
Affiliation:
Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary
U. STADTMÜLLER
Affiliation:
Abt. Math. III, Universität Ulm, 89069 Ulm, Germany
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Abstract

We prove Tauberian theorems from Jp-summability methods of power series type to ordinary convergence, respectively Mp-summability methods of weighted means. Particular cases are the Abel and Cesàro, as well as logarithmic and harmonic summability. Besides numerical series, we also consider orthogonal series with coefficients from [lscr ]2. In the latter case, it turns out that one of our Tauberian conditions is satisfied almost everywhere on the underlying measure space, thereby proving the claim stated in the title.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 1 , February 1999 , pp. 252 - 262
Copyright
The London Mathematical Society 1999

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