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Laplace Transform Type Multipliers for Hankel Transforms

Published online by Cambridge University Press:  20 November 2018

Jorge J. Betancor ,
Teresa Martínez  and
Lourdes Rodríguez-Mesa
Jorge J. Betancor
Affiliation:
Departamento de Análisis Matemático, Universidad de la Laguna, 38271 La Laguna (Sta. Cruz de Tenerife), Spain. e-mail: jbetanco@ull.es, e-mail: lrguez@ull.es
Teresa Martínez
Affiliation:
Departamento de Matemáticas, Faculdad de Ciencias, Universidad Autónoma de Madrid, 28049 Madrid, Spain. e-mail: teresa.martinez@uam.es
Lourdes Rodríguez-Mesa
Affiliation:
Departamento de Análisis Matemático, Universidad de la Laguna, 38271 La Laguna (Sta. Cruz de Tenerife), Spain. e-mail: jbetanco@ull.es, e-mail: lrguez@ull.es
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Abstract

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In this paper we establish that Hankel multipliers of Laplace transform type are bounded from ${{L}^{p}}\left( w \right)$ into itself when $1\,<\,p\,<\infty$, and from ${{L}^{1}}\left( w \right)$ into ${{L}^{1,\infty }}\left( w \right)$ , provided that $w$ is in the Muckenhoupt class ${{A}^{p}}$ on $\left( \left( 0,\,\infty \right),\,dx \right)$.

Keywords

42Hankel transformLaplace transformmultiplierCalderón-Zygmund
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 51 , Issue 4 , 01 December 2008 , pp. 487 - 496
Copyright
Copyright © Canadian Mathematical Society 2008

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