FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2001, VOLUME 7, NUMBER 2, PAGES 533-563
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.
All articles are published in Russian.
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Last modified: October 31, 2001.