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Weighted norm inequalities for the Hankel- and -transformations

Published online by Cambridge University Press:  14 November 2011

S. A. Emara  and
H. P. Heinig
S. A. Emara
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada
H. P. Heinig
Affiliation:
Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada
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Synopsis

We give conditions on pairs of non-negative weight functions u and v which are sufficient that, for 1<p, q <∞,

where T is the Hankel-or the K-transformation.

The proofs are based on a weighted Marcinkiewicz interpolation theorem for linear operators. In the case that T is the Hankel transformation and 1<p≦q <∞, the result is similar to a weighted estimate of Heywood and Rooney [9], but with different weight conditions.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 325 - 333
Copyright
Copyright © Royal Society of Edinburgh 1986

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