Abstract
We introduce the notion of C-semigroup on a Banach space. This notion is intimately relevent to classical Dirichlet forms on Banach spaces. We shall prove a sufficient condition for a semigroup on R d to be a C-semigroup. Then, we prove that C-semigroups satisfy various functional inequalities such as Poincaré inequality, logarithmical Sobolev inequality and Stein-Meyer-Bakry inequalities (Riesz transform).
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Song, S. (1995). C-semigroups on Banach spaces and functional inequalities. In: Azéma, J., Emery, M., Meyer, P.A., Yor, M. (eds) Séminaire de Probabilités XXIX. Lecture Notes in Mathematics, vol 1613. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0094221
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DOI: https://doi.org/10.1007/BFb0094221
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