Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres

Alessio Martini

doi:10.1007/s00209-016-1813-8

Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres

Alessio Martini

Mathematics

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

7 Citations (Scopus)

183 Downloads (Pure)

Abstract

Let b be the Kohn Laplacian acting on (0; j)-forms on the unit sphere in Cn. In a recent paper of Casarino, Cowling, Sikora and the author, a
spectral multiplier theorem of Mihlin{Hormander type for b is proved in the case 0 < j < n 􀀀 1. Here we prove an analogous theorem in the exceptional
cases j = 0 and j = n 􀀀 1, including a weak type (1; 1) endpoint estimate. We also show that both theorems are sharp. The proof hinges on an abstract
multivariate multiplier theorem for systems of commuting operators.

Original language	English
Pages (from-to)	1539-1574
Journal	Mathematische Zeitschrift
Volume	286
Issue number	3-4
Early online date	10 Nov 2016
DOIs	https://doi.org/10.1007/s00209-016-1813-8
Publication status	Published - Aug 2017

Keywords

tangential Cauchy-Riemann complex
multivariable multiplier theorem
Kohn Laplacian
spectral multiplier

Access to Document

10.1007/s00209-016-1813-8Licence: Creative Commons: Attribution (CC BY)

Martini_Joint_functional_calculi_Mathematische_ZeitschriftFinal published version, 781 KBLicence: Creative Commons: Attribution (CC BY)

Cite this

@article{edc41cf36d2641f8ae337397ab3c8754,

title = "Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres",

abstract = "Let b be the Kohn Laplacian acting on (0; j)-forms on the unit sphere in Cn. In a recent paper of Casarino, Cowling, Sikora and the author, aspectral multiplier theorem of Mihlin{Hormander type for b is proved in the case 0 < j < n 􀀀 1. Here we prove an analogous theorem in the exceptionalcases j = 0 and j = n 􀀀 1, including a weak type (1; 1) endpoint estimate. We also show that both theorems are sharp. The proof hinges on an abstractmultivariate multiplier theorem for systems of commuting operators.",

keywords = "tangential Cauchy-Riemann complex, multivariable multiplier theorem, Kohn Laplacian, spectral multiplier",

author = "Alessio Martini",

year = "2017",

month = aug,

doi = "10.1007/s00209-016-1813-8",

language = "English",

volume = "286",

pages = "1539--1574",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer",

number = "3-4",

}

TY - JOUR

T1 - Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres

AU - Martini, Alessio

PY - 2017/8

Y1 - 2017/8

N2 - Let b be the Kohn Laplacian acting on (0; j)-forms on the unit sphere in Cn. In a recent paper of Casarino, Cowling, Sikora and the author, aspectral multiplier theorem of Mihlin{Hormander type for b is proved in the case 0 < j < n 􀀀 1. Here we prove an analogous theorem in the exceptionalcases j = 0 and j = n 􀀀 1, including a weak type (1; 1) endpoint estimate. We also show that both theorems are sharp. The proof hinges on an abstractmultivariate multiplier theorem for systems of commuting operators.

AB - Let b be the Kohn Laplacian acting on (0; j)-forms on the unit sphere in Cn. In a recent paper of Casarino, Cowling, Sikora and the author, aspectral multiplier theorem of Mihlin{Hormander type for b is proved in the case 0 < j < n 􀀀 1. Here we prove an analogous theorem in the exceptionalcases j = 0 and j = n 􀀀 1, including a weak type (1; 1) endpoint estimate. We also show that both theorems are sharp. The proof hinges on an abstractmultivariate multiplier theorem for systems of commuting operators.

KW - tangential Cauchy-Riemann complex

KW - multivariable multiplier theorem

KW - Kohn Laplacian

KW - spectral multiplier

U2 - 10.1007/s00209-016-1813-8

DO - 10.1007/s00209-016-1813-8

M3 - Article

SN - 0025-5874

VL - 286

SP - 1539

EP - 1574

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

IS - 3-4

ER -

Joint functional calculi and a sharp multiplier theorem for the Kohn Laplacian on spheres

Abstract

Keywords

Access to Document

Fingerprint

Cite this