Operator-valued Fourier multiplier theorems on Lp(X) and geometry of Banach spaces |
| |
Authors: | Maria Girardi Lutz Weis |
| |
Affiliation: | a Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA b Mathematisches Institut I, Universität Karlsruhe, Englerstraße 2, 76128 Karlsruhe, Germany |
| |
Abstract: | This paper gives the optimal order l of smoothness in the Mihlin and Hörmander conditions for operator-valued Fourier multiplier theorems. This optimal order l is determined by the geometry of the underlying Banach spaces (e.g. Fourier type). This requires a new approach to such multiplier theorems, which in turn leads to rather weak assumptions formulated in terms of Besov norms. |
| |
Keywords: | Primary 42B15 46E40 46B09 |
本文献已被 ScienceDirect 等数据库收录! |
|