Convolution kernels versus spectral multipliers for sub-Laplacians on groups of polynomial growth

Alessio Martini, Fulvio Ricci, Leonardo Tolomeo

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)
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Abstract

Let L be a sub-Laplacian on a connected Lie group G of polynomial growth. It is well known that, if F:R→C is in the Schwartz class S(R), then the convolution kernel K F(L) of the operator F(L) is in the Schwartz class S(G). Here we prove a sort of converse implication for a class of groups G including all solvable noncompact groups of polynomial growth. We also discuss the problem whether integrability of K F(L) implies continuity of F.

Original languageEnglish
Pages (from-to)1603-1638
Number of pages36
JournalJournal of Functional Analysis
Volume277
Issue number6
Early online date4 Jun 2019
DOIs
Publication statusPublished - 15 Sep 2019

Keywords

  • Lie group
  • Riemann–Lebesgue lemma
  • Schwartz class
  • Sub-Laplacian

ASJC Scopus subject areas

  • Analysis

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