Riesz transforms, fractional power and functional calculus of Schrodinger operators on weighted Lp-spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Assaad, Joyce

关键词: Riesz transforms;    Schrodinger operators;    Fractional powers;    Functional calculus;    Off-diagonal estimates;    Muckenhoupt class;    Reverse Holder class;   

DOI  :  10.1016/j.jmaa.2013.01.024

来源: Elsevier

【 摘 要 】

We consider the Schrodinger operator A = -Delta + V+ - V- on L-p (R-N, wdx) where N >= 3, and w is a weight in some Muckenhoupt class. We study the boundedness of Riesz transform type operators del A(-1/2) andi vertical bar V vertical bar(1/2) A(-1/2) on L-p(R-N, wdx). Our result extends the one of Bui (2010) [14] to signed potentials and treat the case where p >= 2. It also gives a weighted version of our earlier results Assaad (2011)[1], Assaad and Ouhabaz (2012)121 and of the result (Auscher and Ben Ali 2007) [4] to weighted Lebesgue spaces. We study also the boundedness from L-p(R-N, w(p)dx) to Lq (R-N, w(q)dx) of the fractional power A(-alpha/2) and the L-p (R-N wdx)-boundedness of the H-infinity-functional calculus of A. (C) 2013 Elsevier Inc. All rights reserved.

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