Abstract:
In this report there are proved theorems on the boundedness of the convolution operator acting from the space Lp(H′) (p-summable functions on the line with values in the Hilbert space (H′) into the space Lp(H″). There is derived a new version of the Paley–Littlewood Theorem.
Bibliography: 3 items.
Citation:
P. I. Lizorkin, “On a theorem of Marcinkiewicz type for H-valued functions. A continual form of the Paley–Littlewood theorem”, Math. USSR-Sb., 16:2 (1972), 237–243
\Bibitem{Liz72}
\by P.~I.~Lizorkin
\paper On a theorem of Marcinkiewicz type for $H$-valued functions. A~continual form of the Paley--Littlewood theorem
\jour Math. USSR-Sb.
\yr 1972
\vol 16
\issue 2
\pages 237--243
\mathnet{http://mi.mathnet.ru/eng/sm3046}
\crossref{https://doi.org/10.1070/SM1972v016n02ABEH001423}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=380262}
\zmath{https://zbmath.org/?q=an:0233.46043|0248.46027}
Linking options:
https://www.mathnet.ru/eng/sm3046
https://doi.org/10.1070/SM1972v016n02ABEH001423
https://www.mathnet.ru/eng/sm/v129/i2/p229
This publication is cited in the following 2 articles:
S. S. Ajiev, “On the Boundedness of Singular Integral Operators. I”, Proc. Steklov Inst. Math., 243 (2003), 11–38
Garth I. Gaudry, “Littlewood–Paley theorems for sum and difference sets”, Math Proc Camb Phil Soc, 83:1 (1978), 65
Citation in format AMSBIB
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