%0 Journal Article
%T Riesz transform characterization of H^1 spaces associated with certain Laguerre expansions
%A Marcin Preisner
%J Mathematics
%D 2010
%I arXiv
%R 10.1016/j.jat.2011.10.004
%X For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf =-\frac{d^2}{dx^2}f-\frac{alpha}{x}\frac{d}{dx}f+x^2 f. We define an atomic Hardy space H^1_{at}(X), which is a subspace of L^1((0,infty), x^alpha dx). Then we prove that the space H^1_{at}(X) is also characterized by the Riesz transform Rf=\sqrt{\pi}\frac{d}{dx}L^{-1/2}f in the sense that f\in H^1_{at}(X) if and only if f,Rf \in L^1((0,infty),x^alpha dx).
%U http://arxiv.org/abs/1002.3319v3