Mixed norm estimates for the Riesz transforms on the Heisenberg group
type: Item
instance of: scholarly article
title: Mixed norm estimates for the Riesz transforms on the Heisenberg group
zbMATH Open document ID: 1328.22006
author: Pradeep Boggarapu
author: S. Thangavelu
published in: Monatshefte für Mathematik
publication date: 2015-11-06T00:00:00Z
review text: The authors prove weighted mixed norm estimates for Riesz transforms \(R_{j}\), \(j=1,\ldots , d\) on the Heisenberg group \(\mathbb{H}^d\) and Riesz transforms associated to the special Hermite operator. From these mixed norm estimates the authors deduce vector-valued inequalities for sequences of Riesz transforms associated to generalized Grushin operators and Laguerre operators.
Mathematics Subject Classification ID: 22E30
Mathematics Subject Classification ID: 43A80
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 43A90
zbMATH DE Number: 6505114
zbMATH Keywords: Heisenberg group
zbMATH Keywords: Riesz transform
zbMATH Keywords: weighted norm inequality
zbMATH Keywords: Grushin operator
zbMATH Keywords: Laguerre expansion
zbMATH Keywords: special Hermite operator
reviewed by: Koichi Saka
MaRDI profile type: Publication
full work available at URL: s00605-015-0790-z
OpenAlex ID: W1437425553
cites work: Sharp estimates for some functions of the Laplacian on noncompact symmetric spaces
cites work: The convergence of multidimensional Fourier-Bessel series
cites work: A Note on the Boundedness of Riesz Transform for Some Subelliptic Operators
cites work: The spaces \(L^ p\), with mixed norm
cites work: Radial weights and mixed norm inequalities for the disc multiplier
cites work: Singular integral characterizations of Hardy spaces on homogeneous groups
cites work: The Riesz transform for the harmonic oscillator in spherical coordinates
cites work: Vector-valued extensions for fractional integrals of Laguerre expansions
cites work: Fractional integrals on compact Riemannian symmetric spaces of rank one
cites work: The disc multiplier
cites work: About Riesz transforms on the Heisenberg groups
cites work: Approximation Theory and Harmonic Analysis on Spheres and Balls
cites work: Orthogonal polynomials of several variables
cites work: Q4526789
cites work: Radial $A_p$ weights with applications to the disc multiplier and the Bochner-Riesz operators
cites work: Spherical Harmonics, the Weyl Transform and the Fourier Transform on the Heisenberg Group
cites work: Q4307237
cites work: Estimates for translation-invariant operators on spaces with mixed norms
cites work: Riesz transforms and multipliers for the Grushin operator
cites work: Q4356449
cites work: The weighted norm inequality for a class of oscillatory integral operators
cites work: Riesz transforms for multi-dimensional Laguerre function expansions
cites work: Weighted Sobolev orthogonal polynomials on the unit ball
cites work: Mixed norm estimates for the Riesz transforms associated to Dunkl harmonic oscillators
cites work: Mixed norm estimates for the Riesz transforms on \(\mathrm{SU}(2)\)
cites work: Transference principles for radial multipliers
cites work: Revisiting Riesz transforms on Heisenberg groups
cites work: Topics in Harmonic Analysis Related to the Littlewood-Paley Theory. (AM-63)
cites work: Q3142876
cites work: Poisson integrals and Riesz transforms for Hermite function expansions with weights.
cites work: Analysis of the Laplacian on a complete Riemannian manifold
cites work: Q3137751
cites work: An introduction to the uncertainty principle. Hardy's theorem on Lie groups. With a foreword by Gerald B. Folland
DOI: 10.1007/S00605-015-0790-Z
description: scientific article; zbMATH DE number 6505114