|
|||||
|
|
Paley–Littlewood decomposition for sectorial operators and interpolation spaces |
|
| Authors: | Christoph Kriegler Lutz Weis |
| Affiliation: | 1. Laboratoire de Mathématiques (UMR 6620), Université Blaise‐Pascal (Clermont‐Ferrand 2), Campus Universitaire des Cézeaux, Aubière Cedex, France;2. +49 3. 721 4. 6084 5. 3821+49 6. 7650;7. Karlsruher Institut für Technologie, Fakult?t für Mathematik, Institut für Analysis, Karlsruhe, Germany |
| Abstract: | We prove Paley–Littlewood decompositions for the scales of fractional powers of 0‐sectorial operators A on a Banach space which correspond to Triebel–Lizorkin spaces and the scale of Besov spaces if A is the classical Laplace operator on  We use the  ‐calculus, spectral multiplier theorems and generalized square functions on Banach spaces and apply our results to Laplace‐type operators on manifolds and graphs, Schrödinger operators and Hermite expansion. We also give variants of these results for bisectorial operators and for generators of groups with a bounded  ‐calculus on strips. |
| Keywords: | Littlewood Paley theory functional calculus complex and real interpolation spaces Hö rmander type spectral multiplier theorems 42A45 47A60 42B25 47B40 46J15 |
