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On the range and inversion of fractional integrals in weighted spaces

Published online by Cambridge University Press:  14 November 2011

Kenneth F. Andersen
Kenneth F. Andersen
Affiliation:
Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada
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Synopsis

The weight functions w(x) for which the Riemann fractional integral operator Iα is bounded from the Lebesgue space Lp(wp) into Lq(wq), l/q = l/p −, have been characterized by Muckenhoupt and Wheeden. In this paper, we prove an inversion formula for Iα in the context of these weighted spaces and we also characterize the range of Iα as a subset of Lq(wq) Similar results are proved for other fractional integrals. These results may be viewed as weighted analogues of certain results of Stein and Zygmund, Herson and Heywood, Heywood, and Kober who considered the unweighted case, w(x) = l.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 92 , Issue 1-2 , 1982 , pp. 51 - 64
Copyright
Copyright © Royal Society of Edinburgh 1982

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