R
Renming Song
Researcher at University of Illinois at Urbana–Champaign
Publications - 281
Citations - 7029
Renming Song is an academic researcher from University of Illinois at Urbana–Champaign. The author has contributed to research in topics: Bounded function & Boundary (topology). The author has an hindex of 42, co-authored 267 publications receiving 6408 citations. Previous affiliations of Renming Song include University of Michigan & Nankai University.
Papers
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Book
Bernstein Functions: Theory and Applications
TL;DR: In this paper, the authors present a self-contained and unified approach to Bernstein functions and closely related function classes, bringing together old and establishing new connections, and an extensive list of complete Bernstein functions with their representations is provided.
Journal ArticleDOI
Estimates on Green functions and Poisson kernels for symmetric stable processes
Zhen-Qing Chen,Renming Song +1 more
TL;DR: In this article, a symmetric α-stable process X on Rn is a Levy process whose transition density p(t, x − y) relative to the Lebesgue measure is uniquely determined by its Fourier transform ∫ Rn e ix ·ξp(t, x )dx = e−t|ξ| α.
Book
Potential Analysis of Stable Processes and its Extensions
Krzysztof Bogdan,Tomasz Byczkowski,Tadeusz Kulczycki,Michał Ryznar,Renming Song,Zoran Vondraček,Piotr Graczyk,Andrzej Stos +7 more
TL;DR: Boundary potential theory for Schr#x00F6 dinger operators based on fractional Laplacian is proposed in this article, where the potential theory of subordinate Brownian motion is applied to the potential potential theory.
Journal ArticleDOI
Heat kernel estimates for the Dirichlet fractional Laplacian
TL;DR: In this article, the Dirichlet heat kernel of a non-local operator on open sets has been studied and sharp two-sided estimates for the heat kernel have been obtained for C 1.1 open sets.
Book ChapterDOI
Integral Inequalities for Convex Functions of Operators on Martingales
Burgess Davis,Renming Song +1 more
TL;DR: In this paper, the general question underlying both [2] and the present work may be stated as follows: If U and V are operators on M with values in the set of nonnegative A measurable functions on Ω, under what further conditions does