\(L^ p\) multipliers and their \(H^ 1\)-\(L^ 1\) estimates on the Heisenberg group
type: Item
instance of: scholarly article
title: \(L^ p\) multipliers and their \(H^ 1\)-\(L^ 1\) estimates on the Heisenberg group
zbMATH Open document ID: 0868.42006
DOI: 10.4171/RMI/173
author: Chin-Cheng Lin
published in: Revista Matemática Iberoamericana
publication date: 1997-08-18T00:00:00Z
full work available at URL: https://eudml.org/doc/39477
review text: Summary: We give a Hörmander-type sufficient condition on an operator-valued function \(M\) that implies the \(L^p\)-boundedness result for the operator \(T_M\) defined by \((T_MF) \widehat{ }=M\widehat f\) on the \((2n+1)\)-dimensional Heisenberg group \(\mathbb{H}^n\). Here ``\( \widehat{ } \)'' denotes the Fourier transform on \(\mathbb{H}^n\) defined in terms of the Fock representations. We also show the \(H^1\)-\(L^1\) boundedness of \(T_M\), \(|T_Mf|_{L^1}\leq C|f|_{H^1}\), for \(\mathbb{H}^n\) under the same hypotheses of \(L^p\)-boundedness.
Mathematics Subject Classification ID: 42B15
Mathematics Subject Classification ID: 43A22
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 43A30
Mathematics Subject Classification ID: 43A80
zbMATH DE Number: 813823
zbMATH Keywords: \(L^ p\) multipliers
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Fourier transform
zbMATH Keywords: Fock representations
MaRDI profile type: Publication
OpenAlex ID: W2041748775
description: scientific article; zbMATH DE number 813823