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This volume contains translations of papers that originally appeared in the Japanese journal ""Sugaku"". The papers range over a variety of topics, including differential equations with free boundary, singular integral operators, operator algebras, and relations between the Brownian motion on a manifold with function theory. The volume is suitable for graduate students and research mathematicians interested in analysis and differential equations.
Regularity in free boundary problems by G. S. Weiss Behavior of spatial critical points and zeros of solutions of diffusion equations by S. Sakaguchi Martin boundary and boundary Harnack principle for non-smooth domains by H. Aikawa Singular integrals and Littlewood-Paley functions by S. Sato Convergence of metric measure spaces and energy forms by A. Kasue Subfactor theory and its applications: Operator algebras and quantum field theory by Y. Kawahigashi Brownian motion and value distribution theory of holomorphic maps and harmonic maps by A. Atsuji Statistical inference in two-stage sampling by M. Aoshima.