Pseudo Differential Operators And Markov Processes, Volume Ii: Generators And Their Potential Theory

This is the second volume on pseudo-differential operators and Markov processes. In this text two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator; and the potential theory of these semigroups and their generators.

In this volume two topics are discussed: the construction of Feller and L^p–sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators. The first part of the text essentially discusses the analysis of pseudo-differential operators with negative definite symbols and develops a symbolic calculus; in addition, it deals with special approaches, such as subordination in the sense of Bochner. The second part handles capacities, function spaces associated with continuous negative definite functions, L^p –sub-Markovian semigroups in their associated Bessel potential spaces, Stein's Littlewood–Paley theory, global properties of L^p–sub-Markovian semigroups, and estimates for transition functions.

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