1. CMB 2011 (vol 55 pp. 303)
|Atomic Decomposition and Boundedness of Operators on Weighted Hardy Spaces|
In this article, we establish a new atomic decomposition for $f\in L^2_w\cap H^p_w$, where the decomposition converges in $L^2_w$-norm rather than in the distribution sense. As applications of this decomposition, assuming that $T$ is a linear operator bounded on $L^2_w$ and $0
2. CMB 2004 (vol 47 pp. 206)
|The PoincarÃ© Inequality and Reverse Doubling Weights |
We show that Poincar\'e inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains.
Keywords:reverse doubling weights, PoincarÃ© inequality, John domains
3. 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