Paley-Littlewood decomposition for sectorial operators and interpolation spaces

Christoph Kriegler (1, 2) , Lutz Weis (3)

1 LMBP - Laboratoire de Mathématiques Blaise Pascal
2 UCA [2017-2020] - Université Clermont Auvergne [2017-2020]
3 Fakultät für Mathematik, KIT, Allemagne

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 $L^p(\mathbb{R}^n).$ We use the $H^\infty$-calculus, spectral multiplier theorems and generalized square functions on Banach spaces and apply our results to Laplace-type operators on manifolds and graphs, Schr\"odinger operators and Hermite expansion. We also give variants of these results for bisectorial operators and for generators of groups with a bounded $H^\infty$-calculus on strips.

Mots clés: Littlewood-Paley theory; functional calculus; complex and real interpolation spaces; Hörmander type spectral multiplier theorems

Domaines: Analyse fonctionnelle [math.FA]; Théorie spectrale [math.SP]

Christoph Kriegler, Lutz Weis. Paley-Littlewood decomposition for sectorial operators and interpolation spaces. Mathematical News / Mathematische Nachrichten, 2016, ⟨10.1002/mana.201400223⟩. ⟨hal-01017662v2⟩