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Weighted inequalities for the Stieltjes transformation and Hubert's double series

Published online by Cambridge University Press:  14 November 2011

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

The non-negative weight functions U(x), V(x) for which the generalized Stieltjes transformation Sλ is a bounded operator from LP(V) into La(U) are characterized. This extends certain classical inequalities and some recent results of Erdélyi. In particular, our results provide weighted extensions of a classical inequality known as Hubert's double series theorem.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 1-2 , 1980 , pp. 75 - 84
Copyright
Copyright © Royal Society of Edinburgh 1980

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References

1Andersen, K. F. and Muckenhoupt, B.. Weighted weak type Hardy inequalities with applications to Hilbert transforms and maximal functions. Studia Math. 72, in press.Google Scholar
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