Applications of multiresolution analysis in Besov-Q type spaces and Triebel-Lizorkin-Q type spaces

摘要

In this survey, we give a neat summary of the applications of the multi-resolution analysis to the studies of Besov-Q type spaces (B) over dot(p,q)(gamma 1,)(gamma 2) (R-n) and Triebel-Lizorkin-Q type spaces (B) over dot(p,q)(gamma 1,)(gamma 2) (R-n). We will state briefly the recent progress on the wavelet characterizations, the boundedness of CalderonZygmund operators, the boundary value problem (B) over dot(p,q)(gamma 1,)(gamma 2) (R-n) and (F) over dot(p,q)(gamma 1,)(gamma 2) (R-n). We also present the recent developments on the well-posedness of fluid equations with small data in (B) over dot(p,q)(gamma 1,)(gamma 2) (R-n) and (F) over dot(p,q)(gamma 1,)(gamma 2) (R-n).