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2010 $H^1$ BOUNDEDNESS FOR RIESZ TRANSFORM RELATED TO SCHRÖDINGER OPERATOR ON NILPOTENT GROUPS
Yong Ding, Xinfeng Wu
Taiwanese J. Math. 14(4): 1647-1664 (2010). DOI: 10.11650/twjm/1500405975

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.

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Yong Ding. Xinfeng Wu. "$H^1$ BOUNDEDNESS FOR RIESZ TRANSFORM RELATED TO SCHRÖDINGER OPERATOR ON NILPOTENT GROUPS." Taiwanese J. Math. 14 (4) 1647 - 1664, 2010. https://doi.org/10.11650/twjm/1500405975

Information

Published: 2010
First available in Project Euclid: 18 July 2017

zbMATH: 1215.35053
MathSciNet: MR2663939
Digital Object Identifier: 10.11650/twjm/1500405975

Subjects:
Primary: 35J10, 42B30, 42B35

Rights: Copyright © 2010 The Mathematical Society of the Republic of China

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