FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2001, VOLUME 7, NUMBER 2, PAGES 533-563

On Paley-type theorems for multidimensional Fourier series on generalized Haar-type systems

E. S. Smailov

Abstract

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In the paper we prove Paley-type theorems for multidimensional Fourier series on generalized Haar-type systems under the boundedness condition of their generating number sequences. Properties of base of product of generalized Haar-type systems in $L$_p[0,1]ⁿ are proved. Then, using them, the Paley-type theorems on Fourier coefficients are obtained. Comparisons of our results with the known statements are also given.

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Last modified: October 31, 2001.