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 operator m(L,-iT) belongs to L1, then m equals almost everywhere a continuous function vanishing at ∞ (‘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

mattia 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 operator m(L,-iT) belongs to L1, then m equals almost everywhere a continuous function vanishing at ∞ (‘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.
Settore MAT/05 - Analisi Matematica
2-Step stratified group; Riemann–Lebesgue lemma; Schwartz class; Spectral multiplier; Sub-Laplacian;
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embargo fino al 19/03/2021

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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/82588
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