Vector-valued multiparameter singular integrals and pseudodifferential operators |
| |
Authors: | Tuomas Hytö nen,Pierre Portal |
| |
Affiliation: | a Department of Mathematics and Statistics, University of Helsinki, Gustaf Hällströmin katu 2b, FI-00014 Helsinki, Finland b Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia |
| |
Abstract: | We consider multiparameter singular integrals and pseudodifferential operators acting on mixed-norm Bochner spaces Lp1,…,pN(Rn1×?×RnN;X) where X is a UMD Banach space satisfying Pisier's property (α). These geometric conditions are shown to be necessary. We obtain a vector-valued version of a result by R. Fefferman and Stein, also providing a new, inductive proof of the original scalar-valued theorem. Then we extend a result of Bourgain on singular integrals in UMD spaces with an unconditional basis to a multiparameter situation. Finally we carry over a result of Yamazaki on pseudodifferential operators to the Bochner space setting, improving the known vector-valued results even in the one-parameter case. |
| |
Keywords: | 42B20 47G30 46B09 46E40 |
本文献已被 ScienceDirect 等数据库收录! |
|