Calderon's reproducing formula related to the Dunkl operator on the real line

被引：7

作者：

Mourou, MA ^{[1
]}

Trimèche, K ^{[1
]}

机构：

[1] Fac Sci Tunis, Dept Math, Tunis 1060, Tunisia

来源：

MONATSHEFTE FUR MATHEMATIK | 2002年 / 136卷 / 01期

关键词：

differential-difference operators; generalized convolution; Calderon's formula; generalized Hilbert transform;

D O I：

10.1007/s006050200033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a generalized convolution *α, α > -1/2, on the real line generated by the Dunkl operator Λαf = df/dx+(α+1/2)f(x)-f(-x)/x Through this convolution structure, we associate with the differential-difference operator Λα a Calderon type reproducing formula which involves finite Borel measures, and gives rise to new representations for Lp-functions on the real line and their generalized Hilbert transforms.

引用

页码：47 / 65

页数：19

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