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The Ap condition and a positive, linear operator*

Published online by Cambridge University Press:  14 November 2011

Gordon Sinnamon
Gordon Sinnamon
Affiliation:
Department of Mathematics, University of Western Ontario, Middlesex College, London, Ontario, Canada N6A 5B7
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Synopsis

A positive, linear operator is exhibited which is bounded on the mixed weighted Lebesgue space if and only if the weight w satisfies the Ap condition of Muckenhoupt.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 118 , Issue 1-2 , 1991 , pp. 153 - 156
Copyright
Copyright © Royal Society of Edinburgh 1991

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References

1Benedek, A. and Panzone, R.. The spaces L p, with mixed norm. Duke Math. J. 28 (1961), 301–324.CrossRefGoogle Scholar
2García-Cuerva, J. and Rubio de Francia, J. L.. Weighted Norm Inequalities and Related topics, North-Holland Mathematical Studies 116., Notas de Matemética (104) (Amsterdam: Elsevier Science Publishers B. V., 1985).Google Scholar
3Muckenhoupt, B.. Weighted norm inequalities for the Hardy Maximal Function. Trans. Amer. Math. Soc. 165 (1972), 207–226.CrossRefGoogle Scholar