Riesz Transform Characterizations of Hardy Spaces Associated to Degenerate Elliptic Operators

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• 作者：Dachun Yang ; Junqiang Zhang
• 关键词：Primary 47B06 ; Secondary 42B30 ; 42B35 ; 35J70 ; Degenerate elliptic operator ; Hardy space ; Hardy–Sobolev space ; Riesz transform
• 刊名：Integral Equations and Operator Theory
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：84
• 期：2
• 页码：183-216
• 全文大小：821 KB
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• 作者单位：Dachun Yang (1)
  Junqiang Zhang (1)
  
  1. School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, People’s Republic of China
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  
• 出版者：Birkh盲user Basel
• ISSN：1420-8989

文摘

Let \({L_{w}}{:=-w^{-1}{\rm div}(A\nabla)}\) be the degenerate elliptic operator on the Euclidean space \({{\mathbb{R}^{n}}}\), where w is a Muckenhoupt \({A_{2}({\mathbb{R}^{n}})}\) weight. In this article, the authors establish the Riesz transform characterization of the Hardy space \({H^{p}_{L_{w}}({\mathbb{R}}^{n})}\) associated with L _w , for \({w \in A_{q}({\mathbb{R}}^{n}) \cap RH_{\frac{n}{n-2}}({\mathbb{R}^{n}})}\) with \({n \geq 3}\), \({q \in [1,2]}\) and \({p \in (q(\frac{1}{r}+\frac{q-1}{2}+\frac{1}{n})^{-1},1]}\) if, for some \({r \in (1,\,2]}\), \({{\{tL_w e^{-tL_w}\}}_{t\geq 0}}\) satisfies the weighted \({L^{r}-L^{2}}\) full off-diagonal estimates. Keywords Degenerate elliptic operator Hardy space Hardy–Sobolev space Riesz transform