Let L be a homogeneous sublaplacian on a 2-step stratified Lie group G of topological dimension d and homogeneous dimension Q. By a theorem due to Christ and to Mauceri and Meda, an operator of the form F(L) is bounded on L-p for 1 < p < infinity if F satisfies a scale-invariant smoothness condition of order s > Q/2. Under suitable assumptions on G and L, here we show that a smoothness condition of order s > d/2 is sufficient. This extends to a larger class of 2-step groups the results for the Heisenberg and related groups by Muller and Stein and by Hebisch and for the free group N-3,(2) by Muller and the author.

Spectral multipliers on Heisenberg-Reiter and related groups / Martini, A.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - STAMPA. - 194:4(2015), pp. 1135-1155. [10.1007/s10231-014-0414-6]

Spectral multipliers on Heisenberg-Reiter and related groups

Martini A.
2015

Abstract

Let L be a homogeneous sublaplacian on a 2-step stratified Lie group G of topological dimension d and homogeneous dimension Q. By a theorem due to Christ and to Mauceri and Meda, an operator of the form F(L) is bounded on L-p for 1 < p < infinity if F satisfies a scale-invariant smoothness condition of order s > Q/2. Under suitable assumptions on G and L, here we show that a smoothness condition of order s > d/2 is sufficient. This extends to a larger class of 2-step groups the results for the Heisenberg and related groups by Muller and Stein and by Hebisch and for the free group N-3,(2) by Muller and the author.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2949472