Abstract
Let E be a Polish space, M 1(E) be the space of probability measures on E and B(E; ℝ) be the space of bounded measurable real valued functions on E. For a given μ ∈ M 1 (E), we write \( < f{ > _{\mu }} = {\smallint _{E}}fd\mu \) and \( \left \| f \right \|_p=\left \| f \right \|_{Lp(\mu )} \). Let {Pt: t > 0} be a μ-symmetric Markov semigroup on E with generator L. We will suppose that the domain of L contains an algebra A \( \subseteq \) B(E; ℝ) dense in L p(μ), 1 ≤ p < ∞, which is closed under L, P t and the composition of C ∞-functions. Moreover the semigroup should be sufficiently mixing so that for all f ∈ A,
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References
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© 1990 Birkhäuser Boston
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Deuschel, JD. (1990). Logarithmic Sobolev Inequalities of Symmetric Diffusions. In: Çinlar, E., Chung, K.L., Getoor, R.K., Fitzsimmons, P.J., Williams, R.J. (eds) Seminar on Stochastic Processes, 1989. Progress in Probability, vol 18. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3458-6_2
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DOI: https://doi.org/10.1007/978-1-4612-3458-6_2
Publisher Name: Birkhäuser Boston
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