Riesz transform characterization of H1 spaces associated with certain Laguerre expansions

JOURNAL OF APPROXIMATION THEORY

卷:164

Article

Preisner, Marcin

关键词: Hardy space;    Lagueffe operator;    Atomic decomposition;    Riesz transform;   

DOI  :  10.1016/j.jat.2011.10.004

来源: Elsevier

【 摘 要 】

For alpha > 0 we consider the system psi((alpha-1)/2)(k)(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf = -d(2)/dx(2) f - alpha/x d/dx f + x(2)f. We define an atomic Hardy space H-at(1) (X), which is subspace of L-1((0, infinity), x(alpha) dx). Then we prove that the space H-at(1) (X) is also characterized by the Riesz transform Rf = root pi partial derivative/partial derivative x L-1/2 f in the sense that f is an element of H-at(1)/ (X) if and only if f, Rf is an element of L-1 ((0, infinity), x(alpha) dx). (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free