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On the equivalence of weighted inequalities for a class of operators

Published online by Cambridge University Press:  26 September 2011

Dah-Chin Luor
Dah-Chin Luor
Affiliation:
Department of Applied Mathematics, I-Shou University, Dashu District, Kaohsiung City 84001, Taiwan, Republic of China (dclour@isu.edu.tw)
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Abstract

A characterization is obtained on weight function u so that is bounded for 1 < p < ∞ and 0 < q < ∞, where T are integral operators and related maximal operators, and for 0 < p, q < ∞, where T are geometric mean operators and related geometric maximal operators. The equivalence of such weighted inequalities for these operators are established.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 141 , Issue 5 , October 2011 , pp. 1071 - 1081
Copyright
Copyright © Royal Society of Edinburgh 2011

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