185,146 research outputs found
Decompositions of Besov-Hausdorff and Triebel-Lizorkin-Hausdorff Spaces and Their Applications
Let , , and . In this paper, the authors establish the
-transform characterizations of Besov-Hausdorff spaces and Triebel-Lizorkin-Hausdorff spaces (); as applications, the authors then
establish their embedding properties (which on is also sharp), smooth atomic and molecular
decomposition characterizations for suitable . Moreover, using their
atomic and molecular decomposition characterizations, the authors investigate
the trace properties and the boundedness of pseudo-differential operators with
homogeneous symbols in and (), which generalize the corresponding
classical results on homogeneous Besov and Triebel-Lizorkin spaces when
and by taking .Comment: 30 pages, J. Math. Anal. Appl. (to appear)
- β¦