Riesz transforms and multipliers for the Grushin operator

被引：22

作者：

Jotsaroop, K. ^{[1
]}

Sanjay, P. K. ^{[2
]}

Thangavelu, S. ^{[1
]}

机构：

[1] Indian Inst Sci, Dept Math, Bangalore 560012, Karnataka, India

[2] Natl Inst Technol, Dept Math, Calicut 673601, Kerala, India

来源：

JOURNAL D ANALYSE MATHEMATIQUE | 2013年 / 119卷

关键词：

SUMMABILITY;

D O I：

10.1007/s11854-013-0008-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We show that Riesz transforms associated to the Grushin operator G = -Delta - |x|(2 similar to) (t) (2) are bounded on L (p) (a"e (n+1)). We also establish an analogue of the Hormander-Mihlin Multiplier Theorem and study Bochner-Riesz means associated to the Grushin operator. The main tools used are Littlewood-Paley theory and an operator-valued Fourier multiplier theorem due to L. Weis.

引用

页码：255 / 273

页数：19

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