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Commutators and Analytic Dependence of Fourier-Bessel Series on (0, ∞)

Published online by Cambridge University Press:  20 November 2018

José J. Guadalupe ,
Mario Pérez  and
Juan L. Varona
José J. Guadalupe
Affiliation:
Dpto. de Matemáticas y Computaciòn Universidad de La Rioja 26004 Logroño Spain
Mario Pérez
Affiliation:
Dpto. de Matemáticas Universidad de Zaragoza 50009 Zaragoza Spain, email: mperez@posta.unizar.es
Juan L. Varona
Affiliation:
Dpto. de Matemáticas y Computaciòn Universidad de La Rioja 26004 Logroño Spain, email: jvarona@dmc.unirioja.es
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Abstract

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In this paper we study the boundedness of the commutators $[b,\,{{S}_{n}}]$ where $b$ is a $\text{BMO}$ function and ${{S}_{n}}$ denotes the $n$-th partial sum of the Fourier-Bessel series on $(0,\,\infty )$. Perturbing the measure by $\text{exp(}2\text{b)}$ we obtain that certain operators related to ${{S}_{n}}$ depend analytically on the functional parameter $b$.

Keywords

42C10Fourier-Bessel seriescommutatorsBMOAp weights
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 42 , Issue 2 , 01 June 1999 , pp. 198 - 208
Copyright
Copyright © Canadian Mathematical Society 1999

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