arrow
Volume 31, Issue 2
Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces

Hua Wang

Anal. Theory Appl., 31 (2015), pp. 138-153.

Published online: 2017-04

Export citation
  • 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 $w ∈ A_1∩RH_{(2/p)′}$.

  • Keywords

Weighted Hardy space, Riesz transform, Schrödinger operator, atomic decomposition, $A_p$ weight.

  • AMS Subject Headings

42B20, 42B30, 35J10

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{ATA-31-138, author = {}, title = {Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {31}, number = {2}, pages = {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 $w ∈ A_1∩RH_{(2/p)′}$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2015.v31.n2.4}, url = {http://global-sci.org/intro/article_detail/ata/4629.html} }
TY - JOUR T1 - Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces JO - Analysis in Theory and Applications VL - 2 SP - 138 EP - 153 PY - 2017 DA - 2017/04 SN - 31 DO - http://doi.org/10.4208/ata.2015.v31.n2.4 UR - https://global-sci.org/intro/article_detail/ata/4629.html KW - Weighted Hardy space, Riesz transform, Schrödinger operator, atomic decomposition, $A_p$ weight. AB -

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 $w ∈ A_1∩RH_{(2/p)′}$.

Hua Wang. (1970). Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces. Analysis in Theory and Applications. 31 (2). 138-153. doi:10.4208/ata.2015.v31.n2.4
Copy to clipboard
The citation has been copied to your clipboard