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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Some weighted inequalities on product domains


Author: Henry Lin
Journal: Trans. Amer. Math. Soc. 318 (1990), 69-85
MSC: Primary 42B20; Secondary 26D15
DOI: https://doi.org/10.1090/S0002-9947-1990-0970269-1
MathSciNet review: 970269
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Abstract: We extend the results of R. Fefferman [3] on the bidisc to higher product domains via induction. As an application, we extend the weighted inequality for Calderon-Zygmund operators on the bidisc to higher product domains, and we also extend the result of the Littlewood-Paley operator corresponding to the arbitrary disjoint rectangles to the weighted case.


References [Enhancements On Off] (What's this?)

  • [1] José L. Rubio de Francia, A Littlewood-Paley inequality for arbitrary intervals, Mittag-Leffler Institute, Report No. 18, 1983.
  • [2] Jean-Lin Journé, Calderon-Zygmund operators on product spaces, Rev. Mat. Iberoamericana 1 (1985), 55-91. MR 836284 (88d:42028)
  • [3] Robert Fefferman, Harmonic analysis in product spaces, Ann. of Math. (2) 126 (1987), 109-130. MR 898053 (90e:42030)
  • [4] C. Fefferman and E. M. Stein, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115. MR 0284802 (44:2026)
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  • [6] J. Pipher, Journé's covering lemma and its extension to higher dimensions, Duke J. Math. 53 (1986), 683-690. MR 860666 (88a:42019)
  • [7] R. Fefferman, $ {A_p}$ weights and singular integrals, Amer. J. Math. 110 (1988), 975-987. MR 961502 (90b:42033)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1990-0970269-1
Article copyright: © Copyright 1990 American Mathematical Society

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