We prove that if a symmetric submarkovian semigroup (Tt) t>0 satisfies an estimate of the form where theta is an increasing C 1 -diffeomorphism of [0,+infinity) with subexponential growth, then a suitable function of its infinitesimal generator is bounded from L p (M) to L q (M) for 1<p<q<+infinity, and that a weak converse holds true if p=2. In the special case where theta(t)=Ct mi for small t and theta(t)=C' exp(ct v) for large t, mi>0, c>0, 0<v<1, one obtains a sharp and explicit result, which applies for instance to sublaplacians on solvable unimodular Lie groups with exponential growth.

Coulhon, T., & Meda, S. (2003). Subexponential ultracontractivity and Lp-Lq functional calculus. MATHEMATISCHE ZEITSCHRIFT, 244, 291-308 [10.1007/s00209-003-0500-8].

Subexponential ultracontractivity and Lp-Lq functional calculus

MEDA, STEFANO
2003

Abstract

We prove that if a symmetric submarkovian semigroup (Tt) t>0 satisfies an estimate of the form where theta is an increasing C 1 -diffeomorphism of [0,+infinity) with subexponential growth, then a suitable function of its infinitesimal generator is bounded from L p (M) to L q (M) for 10, c>0, 0
Articolo in rivista - Articolo scientifico
Ultracontractive semigroups; solvable Lie groups; functional calculus
English
Coulhon, T., & Meda, S. (2003). Subexponential ultracontractivity and Lp-Lq functional calculus. MATHEMATISCHE ZEITSCHRIFT, 244, 291-308 [10.1007/s00209-003-0500-8].
Coulhon, T; Meda, S
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10281/2187
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