Assume that an operator L1 satisfies a log-Sobolev inequality with parameter on a measure space (X1,μ1), and that another operator L0 satisfies a log-Sobolev inequality (defective or with parameter) on a second measure space (X0,μ0). Then we prove a log-Sobolev inequality (defective or with parameter) for the semi-direct product operator L = L0 + N(x)L1 on the product measure space X1 x X0. Several variants and applications of the results are given in later sections of the paper.
Log-Sobolev inequalities for semi-direct product operators and applications / D'Ancona, Piero Antonio; Pierfelice, Vittoria; Maheux, Patrick. - In: MATHEMATISCHE ZEITSCHRIFT. - ISSN 0025-5874. - STAMPA. - (2016), pp. 103-131.
Log-Sobolev inequalities for semi-direct product operators and applications
D'ANCONA, Piero Antonio;
2016
Abstract
Assume that an operator L1 satisfies a log-Sobolev inequality with parameter on a measure space (X1,μ1), and that another operator L0 satisfies a log-Sobolev inequality (defective or with parameter) on a second measure space (X0,μ0). Then we prove a log-Sobolev inequality (defective or with parameter) for the semi-direct product operator L = L0 + N(x)L1 on the product measure space X1 x X0. Several variants and applications of the results are given in later sections of the paper.| File | Dimensione | Formato | |
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