Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 2, pp. 533-563
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E. S. Smailov. On Paley-type theorems for multidimensional Fourier series on generalized Haar-type systems. Fundamentalʹnaâ i prikladnaâ matematika, Tome 7 (2001) no. 2, pp. 533-563. http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a12/
@article{FPM_2001_7_2_a12,
author = {E. S. Smailov},
title = {On {Paley-type} theorems for multidimensional {Fourier} series on generalized {Haar-type} systems},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {533--563},
year = {2001},
volume = {7},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a12/}
}
TY - JOUR
AU - E. S. Smailov
TI - On Paley-type theorems for multidimensional Fourier series on generalized Haar-type systems
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 2001
SP - 533
EP - 563
VL - 7
IS - 2
UR - http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a12/
LA - ru
ID - FPM_2001_7_2_a12
ER -
%0 Journal Article
%A E. S. Smailov
%T On Paley-type theorems for multidimensional Fourier series on generalized Haar-type systems
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2001
%P 533-563
%V 7
%N 2
%U http://geodesic.mathdoc.fr/item/FPM_2001_7_2_a12/
%G ru
%F FPM_2001_7_2_a12
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.
