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A note on weighted maximal inequalities

Published online by Cambridge University Press:  20 January 2009

Qinsheng Lai
Qinsheng Lai
Affiliation:
Department of Mathematics and Statistics, University of Edinburgh, Edinburgh EH9 3JZ, Scotland
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Abstract

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In this paper, we obtain some characterizations for the weighted weak type (1, q) inequality to hold for the Hardy-Littlewood maximal operator in the case 0<q<1; prove that there is no nontrivial weight satisfying one-weight weak type (p, q) inequalities when 0<p≠q< ∞, and discuss the equivalence between the weak type (p, q) inequality and the strong type (p, q) inequality when p≠q.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 1 , February 1997 , pp. 193 - 205
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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