On double cosine, sine, and Walsh series with monotone coefficients

Author:
Ferenc Móricz

Journal:
Proc. Amer. Math. Soc. **109** (1990), 417-425

MSC:
Primary 42B05; Secondary 42A32

DOI:
https://doi.org/10.1090/S0002-9939-1990-1010803-4

MathSciNet review:
1010803

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Abstract | References | Similar Articles | Additional Information

Abstract: We extend from one-dimensional to two-dimensional series the results by Hardy and Littlewood [6] on the -integrability of the sum and the results by Stechkin [10] on the -integrability of the maximum partial sum in the case of cosine and sine series with monotone coefficients. Among others, we prove that the -integrability of and is essentially equivalent for in the two-dimensional setting, too. Simultaneously, we extend our earlier results in [7] from one-dimensional to two-dimensional Walsh series.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1990-1010803-4

Keywords:
Rectangular partial sum,
maximum partial sum,
pointwise convergence and convergence in -norm in Pringsheim's sense,
Hardy's inequalities for double integrals and double sequences

Article copyright:
© Copyright 1990
American Mathematical Society