Weighted inequalities for iterated convolutions

Author:
Kenneth F. Andersen

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2643-2651

MSC (1991):
Primary 26D15, 44A35, 42A85; Secondary 26D10

Published electronically:
May 4, 1999

MathSciNet review:
1657742

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Abstract | References | Similar Articles | Additional Information

Abstract: Given a fixed exponent , , and suitable nonnegative weight functions , , an optimal associated weight function is constructed for which the iterated convolution product satisfies

for all complex valued measurable functions with . Here and for each , . Analogous results are given when is replaced by and also when the convolution on is taken instead to be . The extremal functions are also discussed.

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Additional Information

**Kenneth F. Andersen**

Affiliation:
Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1

Email:
kanderse@vega.math.ualberta.ca

DOI:
https://doi.org/10.1090/S0002-9939-99-05271-5

Keywords:
Convolution,
weights,
inequalities

Received by editor(s):
June 24, 1997

Published electronically:
May 4, 1999

Additional Notes:
This research was supported in part by NSERC research grant #OGP-8185.

Communicated by:
Frederick W. Gehring

Article copyright:
© Copyright 1999
American Mathematical Society