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 $L^2(\mathbb{R}^n)$, $n ≥ 1$, where $V \not\equiv 0$ is a nonnegative locally integrable function on $\mathbb{R}^n$. In this article, we will introduce weighted Hardy spaces $H^p_L(w)$ associated with $L$ by means of the square function and then study their atomic decomposition theory. We will also show that the Riesz transform $∇L^{−1/2}$ associated with $L$ is bounded from our new space $H^p_L (w)$ to the classical weighted Hardy space $H^p(w)$ when $n/(n+1)< p<1$ and $w ∈ A_1∩RH_{(2/p)′}$.

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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 $A_p$ weight.

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