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Maximal operators associated to Fourier multipliers with an arbitrary set of parameters

Published online by Cambridge University Press:  14 November 2011

Javier Duoandikoetxea  and
Ana Vargas
Javier Duoandikoetxea
Affiliation:
Departamento de Matemáticas, Universidad del País Vasco, Apartado 644,48080, Bilbao, Spain E-mail: mtpduzuj@lg.ehu.es
Ana Vargas
Affiliation:
Department of Mathematics, Yale University, New Haven CT 06520, USA; Departamento de Matemáticas, Universidad Autónoma de Madrid, 28049 Madrid, Spain E-mail: ana.vargas@uam.es
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Abstract

We present here some general results of boundedness on LP for maximal operators of the form , where E is a subset of the positive real numbers and Tt is a dilation of a fixed multiplier operator. The range of values of p depends only on the decay at infinity of the multiplier and the Minkowski dimension of E. For the case being the maximal operator associated to a convex body, we prove that the norm of the operator is independent of the body.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 128 , Issue 4 , 1998 , pp. 683 - 696
Copyright
Copyright © Royal Society of Edinburgh 1998

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