Singular integrals associated to the Laplacian on the affine group \(ax+b\)

DOI10.1007/BF02384874zbMath0776.43003OpenAlexW1976537873MaRDI QIDQ2365890

Tao Qian, Peter Sjögren, Garth I. Gaudry

Publication date: 29 June 1993

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02384874

zbMATH Keywords

affine groupbounded operatorkernels of convolution operatorsright-invariant differential operators

Mathematics Subject Classification ID

Singular and oscillatory integrals (Calderón-Zygmund, etc.) (42B20) Laplace transform (44A10) Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis) (43A65) Analysis on other specific Lie groups (43A80) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15)

Related Items

Global \(L^{p}\) estimates for degenerate Ornstein-Uhlenbeck operators ⋮ Riesz transforms on \(ax+b\) groups ⋮ Equivalent characterizations for boundedness of maximal singular integrals on \(ax+b\)-groups ⋮ Boundedness from \(H^1\) to \(L^1\) of Riesz transforms on a Lie group of exponential growth ⋮ Dyadic sets, maximal functions and applications on \(ax + b\)-groups ⋮ Sobolev algebras on nonunimodular Lie groups ⋮ Spaces \(H^1\) and BMO on \(ax+b\)-groups ⋮ Riesz transforms on solvable extensions of stratified groups ⋮ Estimates for operators related to the sub-Laplacian with drift in Heisenberg groups ⋮ Riesz transforms and Lie groups of polynomial growth ⋮ Asymmetry of convolution norms on Lie groups ⋮ Sharp endpoint estimates for some operators associated with the Laplacian with drift in Euclidean space ⋮ An estimate for a first-order Riesz operator on the affine group

Cites Work

• Analyse sur les groupes de Lie à croissance polynômiale. (Analysis on Lie groups of polynomial growth)
• Analysis of the Laplacian on a complete Riemannian manifold
• Comparaison des champs de vecteurs et des puissances du Laplacien sur une variété Riemannienne à courbure non positive
• Fundamental solutions for second order subelliptic operators
• Sur l'analyse harmonique du groupe affine de la droite
• On the spectrum of the Laplacian on the affine group of the real line
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