Hardy spaces related to Schrodinger operators with potentials which are sums of Lp-functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:396

Article

Dziubanski, Jacek¹  Preisner, Marcin¹ 

[1] Uniwersytet Wroclawski, Inst Matematyczny, PL-50384 Wroclaw, Poland

关键词: Schrodinger operator;    Hardy space;    Maximal function;    Atomic decomposition;    Riesz transform;   

DOI  :  10.1016/j.jmaa.2012.06.012

来源: Elsevier

【 摘 要 】

We investigate the Hardy space H-L(1) associated with the Schrodinger operator L = -Delta + V on R-n, where V = Sigma(d)(j=1) V-j. We assume that each Vj depends on variables from a linear subspace V-j of R-n, dim V-j >= 3, and V-j belongs to L-q (V-j) for certain q. We prove that there exist two distinct isomorphisms of H-L(1) with the classical Hardy space. We deduce as a corollary a specific atomic characterization of H-L(1). We also prove that the space H-L(1) can be described by means of the Riesz transforms R-L.i = partial derivative L-i(-1/2). (C) 2012 Elsevier Inc. All rights reserved.

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