Taiwanese Journal of Mathematics

$H^1$ BOUNDEDNESS FOR RIESZ TRANSFORM RELATED TO SCHRÖDINGER OPERATOR ON NILPOTENT GROUPS

Yong Ding and Xinfeng Wu

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Abstract

Let $\mathbb{G}$ be a nilpotent Lie groups equipped with a Hörmander system of vector fields $X = (X_1,\ldots,X_m)$ and $\Delta = \sum_{i=1}^m X_i^2$ be the sub-Laplacians associated with $X$. Let $A = -\Delta + W$ be the Schrödinger operator with the potential function $W$ belongs to the reverse Hölder class $B_q$ for some $q \ge D/2$, where $D$ denote the dimension at infinity. In this paper, we prove that the Riesz transform $\nabla A^{-1/2}$ related to Schrödinger operator $A$ is bounded from the Hardy space $H^1(\mathbb{G})$ to itself.

Article information

Source
Taiwanese J. Math., Volume 14, Number 4 (2010), 1647-1664.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500405975

Digital Object Identifier
doi:10.11650/twjm/1500405975

Mathematical Reviews number (MathSciNet)
MR2663939

Zentralblatt MATH identifier
1215.35053

Subjects
Primary: 35J10: Schrödinger operator [See also 35Pxx] 42B35: Function spaces arising in harmonic analysis 42B30: $H^p$-spaces

Keywords
Riesz transform Schrödinger operator Hardy space nilpotent groups

Citation

Ding, Yong; Wu, Xinfeng. $H^1$ BOUNDEDNESS FOR RIESZ TRANSFORM RELATED TO SCHRÖDINGER OPERATOR ON NILPOTENT GROUPS. Taiwanese J. Math. 14 (2010), no. 4, 1647--1664. doi:10.11650/twjm/1500405975. https://projecteuclid.org/euclid.twjm/1500405975


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