Holomorphic campanato spaces and a general family of function spaces
Speaker:Dr. Yuan CHENG
Assistant Professor of Institute of Mathematics
School of Science
Tianjin University of Technology and Education
Date & Time:19 Nov 2015 (Thursday) 10:30 - 11:30
Venue:E11-1035
Organized by:Department of Mathematics

Abstract

The class of bounded mean oscillation functions, known as the John-Nirenberg space (BMO), plays crucial role in harmonic analysis and complex analysis. In this talk, we present two kinds of generalization of the BMO. The first is known as Campanato spaces, and the second is the so called general family of function spaces F(p, q, s), or the Zhao’s space. We present the Littlewood-Paley characterization of Campanato spaces and construct the relations between this space and F(p, q, s). We also investigate the boundary value, Corona theorem, and interpolating sequences for a Moebius invariant general family of function spaces. Moreover, we introduce an integral operator preserving the Carleson measures and characterize the distance from the F(p, q, s) spaces to the Bloch-type spaces.

Biography

Dr. Cheng Yuan is currently an associate professor in Institute of Mathematics, School of Science, Tianjin University of Technology. His major interests focus on complex analysis, harmonic analysis and operator theory, especially the analytic properties of various operators on holomorphic spaces.