Singular spherical maximal operators on a class of two step nilpotent Lie groups

DOI10.1007/BF02772226zbMath1054.22007arXivmath/0307042OpenAlexW1990060164WikidataQ115391665 ScholiaQ115391665MaRDI QIDQ1885663

Andreas Seeger, Detlef Müller

Publication date: 11 November 2004

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0307042

zbMATH Keywords

nilpotent groupmaximal operatorHeisenberg group\(L^{p}\)-boundedness

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Nilpotent and solvable Lie groups (22E25) Analysis on other specific Lie groups (43A80)

Related Items (24)

Restriction theorems on Métiver groups associated to joint functional calculus ⋮ Two versions of the Nikodym maximal function on the Heisenberg group ⋮ Rigidity of 2-step Carnot groups ⋮ The circular maximal operator on Heisenberg radial functions ⋮ Complete classification of pseudo \(H\)-type Lie algebras. I ⋮ Singular spherical maximal operators on a class of degenerate two-step nilpotent Lie groups ⋮ Spherical maximal operators on Heisenberg groups: Restricted dilation sets ⋮ Lacunary maximal functions on homogeneous groups ⋮ Algebraic prolongation and rigidity of Carnot groups ⋮ On the Korányi spherical maximal function on Heisenberg groups ⋮ \(L^p-L^q\) estimates for the circular maximal operator on Heisenberg radial functions ⋮ A restriction theorem for Métivier groups ⋮ On the lacunary spherical maximal function on the Heisenberg group ⋮ Pseudo-metric 2-step nilpotent Lie algebras ⋮ A maximal Fourier integral operator and an application ⋮ An optimal theorem for the spherical maximal operator on the Heisenberg group ⋮ Random martingales and localization of maximal inequalities ⋮ Analysis of joint spectral multipliers on Lie groups of polynomial growth ⋮ On the lack of semiconcavity of the subRiemannian distance in a class of Carnot groups ⋮ On the maximal function associated to the spherical means on the Heisenberg group ⋮ Configuration sets with nonempty interior ⋮ \(L^p\)-Sobolev estimates for a class of integral operators with folding canonical relations ⋮ Spherical means on the Heisenberg group: stability of a maximal function estimate ⋮ New Brezis-van Schaftingen-Yung-Sobolev type inequalities connected with maximal inequalities and one parameter families of operators

Cites Work

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• Hypoellipticite analytique sur des groupes nilpotents de rang 2
• \(L^2\) estimates for averaging operators along curves with two-sided \(k\)-fold singularities
• Pointwise ergodic theorems for radial averages on the Heisenberg group
• Oscillatory integrals and multipliers on FL\(^p\)
• Local Smoothing of Fourier Integral Operators and Carleson-Sjolin Estimates
• Maximal functions: Spherical means
• Fundamental Solutions for a Class of Hypoelliptic PDE Generated by Composition of Quadratic Forms
• Fourier integral operators with fold singularities.
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28

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