Principal values for Riesz transforms and rectifiability

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• 作者：Xavier Tolsa
• 关键词：Riesz transforms ; Principal values ; Rectifiability ; Lipschitz graphs
• 刊名：Journal of Functional Analysis
• 出版年：2008
• 出版时间：1 April 2008
• 年：2008
• 卷：254
• 期：7
• 页码：1811-1863
• 全文大小：394 K

文摘

Let che/MiamiImageURL/B6WJJ-4PRRHJB-2-2/0?wchp=dGLbVzz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=15 width=51> with che/MiamiImageURL/B6WJJ-4PRRHJB-2-4/0?wchp=dGLbVzz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=15 width=82>, where 80574e"">che/MiamiImageURL/B6WJJ-4PRRHJB-2-5/0?wchp=dGLbVzz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=13 width=21> stands for the n-dimensional Hausdorff measure. In this paper we prove that E is n-rectifiable if and only if the limit

exists che/MiamiImageURL/B6WJJ-4PRRHJB-2-7/0?wchp=dGLbVzz-zSkWb"" alt=""Click to view the MathML source"" align=""absbottom"" border=""0"" height=13 width=21>-almost everywhere in E. To prove this result we obtain precise estimates from above and from below for the L² norm of the n-dimensional Riesz transforms on Lipschitz graphs.