Recent Developments of Function Spaces and Their Applications I

Abstract

This book includes 13 papers concerning some of the recent progress in the theory of function spaces and its applications. The involved function spaces include Morrey and weak Morrey spaces, Hardy-type spaces, John–Nirenberg spaces, Sobolev spaces, and Besov and Triebel–Lizorkin spaces on different underlying spaces, and they are applied in the study of problems ranging from harmonic analysis to potential analysis and partial differential equations, such as the boundedness of paraproducts and Calderón operators, the characterization of pointwise multipliers, estimates of anisotropic logarithmic potential, as well as certain Dirichlet problems for the Schrödinger equation.