Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory

• Autorzy: Mark Veraar , Lutz Weis
• Języki publikacji: EN

Abstrakty

EN

We consider generalized square function norms of holomorphic functions with values in a Banach space. One of the main results is a characterization of embeddings of the form
$L^{p}(X) ⊆ γ(X) ⊆ L^{q}(X)$,
in terms of the type p and cotype q of the Banach space X. As an application we prove $L^{p}$-estimates for vector-valued Littlewood-Paley-Stein g-functions and derive an embedding result for real and complex interpolation spaces under type and cotype conditions.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 47D07: Markov semigroups and applications to diffusion processes
• 46B20: Geometry and structure of normed linear spaces
• 46B70: Interpolation between normed linear spaces
• 42B25: Maximal functions, Littlewood-Paley theory
• 46B09: Probabilistic methods in Banach space theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 228
• Numer: 1
• Strony: 73-99

Daty

wydano

2015

Twórcy

autor

Mark Veraar

• Delft Institute of Applied Mathematics, Delft University of Technology, P.O. Box 5031, 2600 GA Delft, The Netherlands

autor

Lutz Weis

• Institut für Analysis, Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany

Identyfikatory

DOI

10.4064/sm228-1-7