Spectral multipliers on 2-step groups: topological versus homogeneous dimension

Martini, A.; Muller, D.

doi:10.1007/s00039-016-0365-8

Let G be a 2-step stratified group of topological dimension d and homogeneous dimension Q. Let L be a homogeneous sub-Laplacian on G. By a theorem due to Christ and to Mauceri and Meda, an operator of the form F(L) is of weak type (1, 1) and bounded on Lp(G) for all p ∈ (1, ∞) whenever the multiplier F satisfies a scale-invariant smoothness condition of order s > Q/2. It is known that, for several 2-step groups and sub-Laplacians, the threshold Q/2 in the smoothness condition is not sharp and in many cases it is possible to push it down to d/2. Here we show that, for all 2-step groups and sub-Laplacians, the sharp threshold is strictly less than Q/2, but not less than d/2.

Spectral multipliers on 2-step groups: topological versus homogeneous dimension / Martini, A.; Muller, D.. - In: GEOMETRIC AND FUNCTIONAL ANALYSIS. - ISSN 1016-443X. - STAMPA. - 26:2(2016), pp. 680-702. [10.1007/s00039-016-0365-8]

Titolo:	Spectral multipliers on 2-step groups: topological versus homogeneous dimension
Autori:	MARTINI, ALESSIO Muller D. mostra contributor esterni nascondi contributor esterni
Data di pubblicazione:	2016
Rivista:	GEOMETRIC AND FUNCTIONAL ANALYSIS
Digital Object Identifier (DOI):	http://dx.doi.org/10.1007/s00039-016-0365-8
Appare nelle tipologie:	1.1 Articolo in rivista

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