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Search: MSC category 42C10 ( Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) )

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1. CMB 2004 (vol 47 pp. 475)

 Uniqueness of Almost Everywhere Convergent Vilenkin Series D. J. Grubb [3] has shown that uniqueness holds, under a mild growth condition, for Vilenkin series which converge almost everywhere to zero. We show that, under even less restrictive growth conditions, one can replace the limit function 0 by an arbitrary $f\in L^q$, when $q>1$. Categories:43A75, 42C10
 Commutators and Analytic Dependence of Fourier-Bessel Series on $(0,\infty)$ 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, $A_p$ weightsCategory:42C10
 A general approach to Littlewood-Paley theorems for orthogonal families A general lacunary Littlewood-Paley type theorem is proved, which applies in a variety of settings including Jacobi polynomials in $[0, 1]$, $\su$, and the usual classical trigonometric series in $[0, 2 \pi)$. The theorem is used to derive new results for $\LP$ multipliers on $\su$ and Jacobi $\LP$ multipliers. Categories:42B25, 42C10, 43A80