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 Mat. Zametki, 1977, Volume 22, Issue 6, Pages 873–884 (Mi mz8108)

Boundedness of the convolution operator in $L_p(Z^m)$ and smoothness of the symbol of the operator

S. L. Edelstein

Rostov State University

Abstract: 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.

Full text: PDF file (839 kB)

English version:
Mathematical Notes, 1977, 22:6, 978–984

Bibliographic databases:

UDC: 517.5

Citation: S. L. Edelstein, “Boundedness of the convolution operator in $L_p(Z^m)$ and smoothness of the symbol of the operator”, Mat. Zametki, 22:6 (1977), 873–884; Math. Notes, 22:6 (1977), 978–984

Citation in format AMSBIB
\Bibitem{Ede77}
\by S.~L.~Edelstein
\paper Boundedness of the convolution operator in $L_p(Z^m)$ and smoothness of the symbol of the operator
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 6
\pages 873--884
\mathnet{http://mi.mathnet.ru/mz8108}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=487596}
\zmath{https://zbmath.org/?q=an:0398.47031}
\transl
\jour Math. Notes
\yr 1977
\vol 22
\issue 6
\pages 978--984
\crossref{https://doi.org/10.1007/BF01099568}