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Functional Inequalities for Some Generalised Mehler Semigroups

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Abstract

We consider generalised Mehler semigroups and, assuming the existence of an associated invariant measure \(\sigma \), we prove functional integral inequalities with respect to \(\sigma \), such as logarithmic Sobolev and Poincaré type. Consequently, some integrability properties of exponential functions with respect to \(\sigma \) are deduced.

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Acknowledgements

The authors are grateful to Alessandra Lunardi and Enrico Priola for many helpful conversations.

Funding

S.F. has been partially supported by the OK-INSAID project ARS01-00917. The authors are members of G.N.A.M.P.A. of the Italian Istituto Nazionale di Alta Matematica (INdAM) and have been partially supported by the PRIN 2015 MIUR project 2015233N54. The authors have no relevant financial or non-financial interests to disclose.

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Authors and Affiliations

  1. Dipartimento di Matematica e Fisica Ennio De Giorgi, Università del Salento, Via per Arnesano, 73100, Lecce, Italy

    Luciana Angiuli, Simone Ferrari & Diego Pallara

  2. I.N.F.N., Sezione di Lecce, Via per Arnesano, 73100, Lecce, Italy

    Diego Pallara

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  1. Luciana Angiuli
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  2. Simone Ferrari
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  3. Diego Pallara
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Correspondence to Simone Ferrari.

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Angiuli, L., Ferrari, S. & Pallara, D. Functional Inequalities for Some Generalised Mehler Semigroups. J Theor Probab 36, 1762–1796 (2023). https://doi.org/10.1007/s10959-022-01215-8

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