Given a 2-step stratified group which does not satisfy a slight strengthening of the Moore-Wolf condition, a sub-Laplacian L and a family T of elements of the derived algebra, we study the convolution kernels associated with the operators of the form m(L,- iT). Under suitable conditions, we prove that: (i) if the convolution kernel of the operatorm(L,- iT) belongs to L1, thenm equals almost everywhere a continuous function vanishing at 8 Riemann-Lebesgue lemma'); (ii) if the convolution kernel of the operator m(L,- iT) is a Schwartz function, then m equals almost everywhere a Schwartz function.

Spectral Multipliers on 2-Step Stratified Groups, I / M. Calzi. - In: JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS. - ISSN 1069-5869. - 26:2(2020 Apr 01). [10.1007/s00041-020-09740-y]

Spectral Multipliers on 2-Step Stratified Groups, I

M. Calzi
2020

Abstract

Given a 2-step stratified group which does not satisfy a slight strengthening of the Moore-Wolf condition, a sub-Laplacian L and a family T of elements of the derived algebra, we study the convolution kernels associated with the operators of the form m(L,- iT). Under suitable conditions, we prove that: (i) if the convolution kernel of the operatorm(L,- iT) belongs to L1, thenm equals almost everywhere a continuous function vanishing at 8 Riemann-Lebesgue lemma'); (ii) if the convolution kernel of the operator m(L,- iT) is a Schwartz function, then m equals almost everywhere a Schwartz function.
spectral multiplier; 2-Step stratified group; Sub-Laplacian; Schwartz class; Riemann-Lebesgue lemma
Settore MAT/05 - Analisi Matematica
1-apr-2020
19-mar-2020
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/722313
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