On the 𝐿²→𝐿^{∞} norms of spectral multipliers of “quasi-homogeneous” operators on homogeneous groups

DOI10.1090/S0002-9947-99-02501-5zbMath0936.42009OpenAlexW1530241702MaRDI QIDQ4252951

Adam S. Sikora

Publication date: 23 June 1999

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-99-02501-5

zbMATH Keywords

Plancherel measurespectral multiplierquasi-homogeneous operatorleft-invariant vector fieldnilpotent homogeneous Lie groupsubelliptic second-order differential operator

Mathematics Subject Classification ID

Spectral theory and eigenvalue problems for partial differential equations (35P99) Multipliers for harmonic analysis in several variables (42B15) Homomorphisms and multipliers of function spaces on groups, semigroups, etc. (43A22)

Related Items (10)

A note on the heat kernel on the Heisenberg group ⋮ \(L^p\)-bounds for Stein's square functions associated to operators and applications to spectral multipliers ⋮ Restriction estimates, sharp spectral multipliers and endpoint estimates for Bochner-Riesz means ⋮ Spectral summability for the quartic oscillator with applications to the Engel group ⋮ Weighted norm inequalities, Gaussian bounds and sharp spectral multipliers ⋮ Commutators of BMO functions with spectral multiplier operators ⋮ Littlewood-Paley and spectral multipliers on weighted \(L^p\) spaces ⋮ Analysis of joint spectral multipliers on Lie groups of polynomial growth ⋮ Functional calculus on non-homogeneous operators on nilpotent groups ⋮ Plancherel-type estimates and sharp spectral multipliers

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