1. CMB 2004 (vol 47 pp. 475)
|Uniqueness of Almost Everywhere Convergent Vilenkin Series |
D. J. Grubb  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 $q>1$.
2. CMB 1999 (vol 42 pp. 198)
|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, $A_p$ weights
3. CMB 1997 (vol 40 pp. 296)
|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