Hörmander's HP multiplier theorem for the Heisenberg group

Chin Cheng Lin

doi:10.1112/S0024610703004150

Hörmander's H^P multiplier theorem for the Heisenberg group

Chin Cheng Lin

Department of Mathematics

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

9 Scopus citations

Abstract

Let ℍⁿ denote the (2n + 1)-dimensional Heisenberg group. Given an operator-valued function M, define the operator T_M by (T_Mf)̂ = f̂M with '̂' denoting the Fourier transform. Hörmander-type sufficient conditions are determined on M for the H^p-boundedness, p ≤ 1, of the operator T_M on ℍⁿ.

Original language	English
Pages (from-to)	686-700
Number of pages	15
Journal	Journal of the London Mathematical Society
Volume	67
Issue number	3
DOIs	https://doi.org/10.1112/S0024610703004150
State	Published - Jun 2003

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title = "H{\"o}rmander's HP multiplier theorem for the Heisenberg group",

abstract = "Let ℍn denote the (2n + 1)-dimensional Heisenberg group. Given an operator-valued function M, define the operator TM by (TMf{\^)} = {\^f}M with {\^'}' denoting the Fourier transform. H{\"o}rmander-type sufficient conditions are determined on M for the Hp-boundedness, p ≤ 1, of the operator TM on ℍn.",

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T1 - Hörmander's HP multiplier theorem for the Heisenberg group

AU - Lin, Chin Cheng

PY - 2003/6

Y1 - 2003/6

N2 - Let ℍn denote the (2n + 1)-dimensional Heisenberg group. Given an operator-valued function M, define the operator TM by (TMf)̂ = f̂M with '̂' denoting the Fourier transform. Hörmander-type sufficient conditions are determined on M for the Hp-boundedness, p ≤ 1, of the operator TM on ℍn.

AB - Let ℍn denote the (2n + 1)-dimensional Heisenberg group. Given an operator-valued function M, define the operator TM by (TMf)̂ = f̂M with '̂' denoting the Fourier transform. Hörmander-type sufficient conditions are determined on M for the Hp-boundedness, p ≤ 1, of the operator TM on ℍn.

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U2 - 10.1112/S0024610703004150

DO - 10.1112/S0024610703004150

M3 - 期刊論文

AN - SCOPUS:0037562807

SN - 0024-6107

VL - 67

SP - 686

EP - 700

JO - Journal of the London Mathematical Society

JF - Journal of the London Mathematical Society

IS - 3

ER -

Hörmander's HP multiplier theorem for the Heisenberg group

Abstract

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Hörmander's H^P multiplier theorem for the Heisenberg group