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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On restriction of maximal multipliers in weighted settings


Authors: María J. Carro and Salvador Rodríguez-López
Journal: Trans. Amer. Math. Soc. 364 (2012), 2241-2260
MSC (2010): Primary 42B15, 42B35
Published electronically: January 19, 2012
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Abstract: We obtain restriction results of K. De Leeuw's type for maximal operators defined through Fourier multipliers of either strong or weak type for weighted $ L^p$ spaces with $ 1\le p<\infty $. Applications to the case of Hörmander-Mihlin multipliers, singular integral operators and Bochner-Riesz sums are given.


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Additional Information

María J. Carro
Affiliation: Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, 08007 Barcelona, Spain
Email: carro@ub.edu

Salvador Rodríguez-López
Affiliation: Department of Mathematics, Uppsala University, Upssala, SE 75106, Sweden
Email: salvador@math.uu.se

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05598-X
PII: S 0002-9947(2012)05598-X
Keywords: Weighted $L^{p}$ spaces, Fourier multipliers
Received by editor(s): July 13, 2009
Published electronically: January 19, 2012
Additional Notes: This work was partially supported by MTM2010-14946. The second author was also partially supported by EP/H051368/1
Article copyright: © Copyright 2012 American Mathematical Society