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 $0 Keywords:$A_p$weights, atomic decomposition, CalderÃ³n reproducing formula, weighted Hardy spacesCategories:42B25, 42B30 2. CMB 2004 (vol 47 pp. 206) Hurri-Syrjänen, Ritva  The PoincarÃ© Inequality and Reverse Doubling Weights We show that Poincar\'e inequalities with reverse doubling weights hold in a large class of irregular domains whenever the weights satisfy certain conditions. Examples of these domains are John domains. Keywords:reverse doubling weights, PoincarÃ© inequality, John domainsCategory:46E35 3. CMB 1999 (vol 42 pp. 198) Guadalupe, José J.; Pérez, Mario; Varona, Juan L.  Commutators and Analytic Dependence of Fourier-Bessel Series on$(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