On certain convolution inequalities

Author:
Lars Inge Hedberg

Journal:
Proc. Amer. Math. Soc. **36** (1972), 505-510

MSC:
Primary 46E30; Secondary 46E35

MathSciNet review:
0312232

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Abstract: It is proved that certain convolution inequalities are easy consequences of the Hardy-Littlewood-Wiener maximal theorem. These inequalities include the Hardy-Littlewood-Sobolev inequality for fractional integrals, its extension by Trudinger, and an interpolation inequality by Adams and Meyers. We also improve a recent extension of Trudinger's inequality due to Strichartz.

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DOI:
http://dx.doi.org/10.1090/S0002-9939-1972-0312232-4

Article copyright:
© Copyright 1972
American Mathematical Society