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# Commutators and Analytic Dependence of Fourier-Bessel Series on $(0,\infty)$

Published:1999-06-01
Printed: Jun 1999
• Mario Pérez
• Juan L. Varona
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## Abstract

In this paper we study the boundedness of the commutators $[b, S_n]$ where $b$ is a $\BMO$ function and $S_n$ denotes the $n$-th partial sum of the Fourier-Bessel series on $(0,\infty)$. Perturbing the measure by $\exp(2b)$ we obtain that certain operators related to $S_n$ depend analytically on the functional parameter $b$.
 Keywords: Fourier-Bessel series, commutators, BMO, $A_p$ weights
 MSC Classifications: 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)