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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
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.
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- The London Mathematical Society 1999