Riesz transforms and Lie groups of polynomial growth

A.F.M. Elst, ter; D.W. Robinson; A. Sikora

doi:10.1006/jfan.1998.3361

Riesz transforms and Lie groups of polynomial growth

A.F.M. Elst, ter, D.W. Robinson, A. Sikora

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

20 Citations (Scopus)

Abstract

Let G be 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 - 1999

Access to Document

10.1006/jfan.1998.3361

Cite this

@article{6c3f14f3ae6d4a5c874ce6b7d5992bc3,

title = "Riesz transforms and Lie groups of polynomial growth",

abstract = "Let G be 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.",

author = "{Elst, ter}, A.F.M. and D.W. Robinson and A. Sikora",

year = "1999",

doi = "10.1006/jfan.1998.3361",

language = "English",

volume = "162",

pages = "14--51",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - Riesz transforms and Lie groups of polynomial growth

AU - Elst, ter, A.F.M.

AU - Robinson, D.W.

AU - Sikora, A.

PY - 1999

Y1 - 1999

N2 - Let G be 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 - Let G be 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.

U2 - 10.1006/jfan.1998.3361

DO - 10.1006/jfan.1998.3361

M3 - Article

SN - 0022-1236

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

Abstract

Access to Document

Fingerprint

Cite this