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 Fourier-Bessel series, commutators, BMO, $A_p$ weights

MSC Classifications:

42C10 show english descriptions Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) 42C10 - Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)

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