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.
Citazione: | Coulhon, T., & Meda, S. (2003). Subexponential ultracontractivity and Lp-Lq functional calculus. MATHEMATISCHE ZEITSCHRIFT, 244, 291-308. |
Tipo: | Articolo in rivista - Articolo scientifico |
Carattere della pubblicazione: | Scientifica |
Titolo: | Subexponential ultracontractivity and Lp-Lq functional calculus |
Autori: | Coulhon, T; Meda, S |
Autori: | |
Data di pubblicazione: | 2003 |
Lingua: | English |
Rivista: | MATHEMATISCHE ZEITSCHRIFT |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1007/s00209-003-0500-8 |
Appare nelle tipologie: | 01 - Articolo su rivista |