A nicely behaved singular integral on a purely unrectifiable set期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

A nicely behaved singular integral on a purely unrectifiable set

Authors:	Petri Huovinen

Affiliation:	Department of Mathematics, University of Jyväskylä, P.O. Box 35, FIN-40351 Jyväskylä, Finland

Abstract:	We construct an example of a purely 1-unrectifiable AD-regular set in the plane such that the limit $begin{displaymath}lim_{rdownarrow 0} intlimits_{Esetminus B(x,r)} K(x-y) , d mathcal{H}^1 (y) end{displaymath}$ exists and is finite for $mathcal{H}^1$ almost every for some class of antisymmetric Calderón-Zygmund kernels. Moreover, the singular integral operators associated with these kernels are bounded in , where has a positive $mathcal{H}^1$ measure.

Keywords:	Singular integrals rectifiability

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