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Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces

Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces

Year:    2015

Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 138–153

Abstract

Let L=+V be a Schrödinger operator acting on L2(Rn), n1, where V0 is a nonnegative locally integrable function on Rn. In this article, we will introduce weighted Hardy spaces HpL(w) associated with L by means of the square function and then study their atomic decomposition theory. We will also show that the Riesz transform L1/2 associated with L is bounded from our new space HpL(w) to the classical weighted Hardy space Hp(w) when n/(n+1)<p<1 and wA1RH(2/p).

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2015.v31.n2.4

Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 138–153

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Weighted Hardy space Riesz transform Schrödinger operator atomic decomposition Ap weight.

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