Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 873-884
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S. L. Edelstein. Boundedness of the convolution operator in $L_p(Z^m)$ and smoothness of the symbol of the operator. Matematičeskie zametki, Tome 22 (1977) no. 6, pp. 873-884. http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a8/
@article{MZM_1977_22_6_a8,
author = {S. L. Edelstein},
title = {Boundedness of the convolution operator in $L_p(Z^m)$ and smoothness of the symbol of the operator},
journal = {Matemati\v{c}eskie zametki},
pages = {873--884},
year = {1977},
volume = {22},
number = {6},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a8/}
}
TY - JOUR
AU - S. L. Edelstein
TI - Boundedness of the convolution operator in $L_p(Z^m)$ and smoothness of the symbol of the operator
JO - Matematičeskie zametki
PY - 1977
SP - 873
EP - 884
VL - 22
IS - 6
UR - http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a8/
LA - ru
ID - MZM_1977_22_6_a8
ER -
%0 Journal Article
%A S. L. Edelstein
%T Boundedness of the convolution operator in $L_p(Z^m)$ and smoothness of the symbol of the operator
%J Matematičeskie zametki
%D 1977
%P 873-884
%V 22
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1977_22_6_a8/
%G ru
%F MZM_1977_22_6_a8
Sufficient conditions for the boundedness of the convolution operator in $L_p(Z^m)$ are found. These conditions are imposed on the symbol of the operator in terms of the spaces $H_\alpha$ and $H_\beta$ (functions of bounded variation of order $\beta$). The results obtained here generalize the results of S. B. Stechkin and I. I. Hirschman [Ref. Zh. Mat.7, No. 7821 (1960)] for the one-dimensional case.
