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Sharp function estimates for fractional integrals and related operators

Part of: Harmonic analysis in several variables Integral transforms, operational calculus Real functions

Published online by Cambridge University Press:  09 April 2009

Douglas S. Kurtz
Douglas S. Kurtz
Affiliation:
New Mexico State UniversityLas Cruces, New Mexico 88003-0001, U.S.A.
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Abstract

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This paper considers analogs of results on integral operators studied by Hörmander. Using the sharp function introduced by Fefferman and Stein, we prove weighted norm inequalities on kernel operators which map an Lp space into an Lq space, with q not equal to p. The techniques recover known results about fractional integral operators and apply to multiplier operators which satisfy a generalization of the Hörmander multiplier condition.

MSC classification

Secondary: 26A33: Fractional derivatives and integrals 42B15: Multipliers 44A35: Convolution
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 49 , Issue 1 , August 1990 , pp. 129 - 137
Copyright
Copyright © Australian Mathematical Society 1990

References

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