Titlebook: Real Analysis Methods for Markov Processes; Singular Integrals a Kazuaki Taira Book 2024 The Editor(s) (if applicable) and The Author(s), u

和善

書目名稱Real Analysis Methods for Markov Processes影響因子(影響力)




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書目名稱Real Analysis Methods for Markov Processes讀者反饋學(xué)科排名

敵手

methods for the study of Markov processes.Furnishes a profou.This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory. Analytically, a Markovian particle in a domain of Euclidean space is governed by an integro-diff

agonist

Besov Spaces via Poisson Integralsev spaces of . type. We prove a variety of equivalent norms for the Besov spaces on . via Poisson integrals (Theorems ., . and .). The results discussed here are adapted from Taibleson [146] and Stein [137].

廚師

Elements of Singular Integrals a straightforward treatment of the Calderón–Zygmund theory necessary for the study of elliptic boundary value problems, assuming only basic knowledge of real analysis and functional analysis. The results discussed here are adapted from Calderón–Zygmund [22–25, 28] and Tanabe [166, 167].

革新

Calderón–Zygmund Variable Kernels and Their Commutatorsvariable kernel case to the constant kernel case. This is done by expanding the kernel into a series of spherical harmonics (Theorem 4.41), each term defining a constant kernel operator treated in Chap. 10.

紳士

Dirichlet Problems in Sobolev Spacesrichlet problem (Theorem 15.1) in Chap. 15. The results discussed here are adapted from Chiarenza–Frasca–Longo [34, 35] and Chiarenza [33]. Our approach can be traced back to the pioneering work of J. Schauder [127, 128] on the Dirichlet problem for second order, elliptic differential operators.

核心

Calderón–Zygmund Kernels and Interior Estimateso Eugenio Elia Levi [89] (Theorem .). The vanishing mean oscillation (VMO) assumption on the coefficients is of the greatest relevance in the study of an error term expressed by singular commutators (Corollary 11.7). The desired interior . estimate (12.2) follows in a standard way from Lemma 13.2. by a covering argument.

為現(xiàn)場(chǎng)

慎重

磨碎

Elements of Functional Analysis (bounded) linear operators between Banach spaces. Most of the material will be quite familiar to the reader and may be omitted. This chapter, included for the sake of completeness, should serve to settle questions of notation and such.