Riesz Transforms and Lie Groups of Polynomial Growth

A. F.M. Ter Elst; Derek W. Robinson; Adam Sikora

doi:10.1006/jfan.1998.3361

Riesz Transforms and Lie Groups of Polynomial Growth

A. F.M. Ter Elst^*, Derek W. Robinson, Adam Sikora

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

Abstract

LetGbe a Lie group of polynomial growth. We prove that the second-order Riesz transforms onL₂(G;dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.

Original language	English
Pages (from-to)	14-51
Number of pages	38
Journal	Journal of Functional Analysis
Volume	162
Issue number	1
DOIs	https://doi.org/10.1006/jfan.1998.3361
Publication status	Published - 20 Feb 1999

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title = "Riesz Transforms and Lie Groups of Polynomial Growth",

abstract = "LetGbe a Lie group of polynomial growth. We prove that the second-order Riesz transforms onL2(G;dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.",

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AU - Ter Elst, A. F.M.

AU - Robinson, Derek W.

AU - Sikora, Adam

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N2 - LetGbe a Lie group of polynomial growth. We prove that the second-order Riesz transforms onL2(G;dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.

AB - LetGbe a Lie group of polynomial growth. We prove that the second-order Riesz transforms onL2(G;dg) are bounded if, and only if, the group is a direct product of a compact group and a nilpotent group, in which case the transforms of all orders are bounded.

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U2 - 10.1006/jfan.1998.3361

DO - 10.1006/jfan.1998.3361

M3 - Article

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VL - 162

SP - 14

EP - 51

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 1

ER -

Riesz Transforms and Lie Groups of Polynomial Growth

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