Geodesic
Estimates for vector-valued holomorphic functions and Littlewood–Paley–Stein theory
Mark Veraar1 ; Lutz Weis2
1 Delft Institute of Applied Mathematics Delft University of Technology P.O. Box 5031 2600 GA Delft, The Netherlands
2 Institut für Analysis Karlsruhe Institute of Technology D-76128 Karlsruhe, Germany
Studia Mathematica, Tome 228 (2015) no. 1, pp. 73-99

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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 \[ L^p(X)\subseteq \gamma (X) \subseteq L^q(X), \] 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.
DOI : 10.4064/sm228-1-7
Keywords: consider generalized square function norms holomorphic functions values banach space main results characterization embeddings form subseteq gamma subseteq terms type cotype banach space application prove p estimates vector valued littlewood paley stein g functions derive embedding result real complex interpolation spaces under type cotype conditions

Mark Veraar 1 ; Lutz Weis 2

1 Delft Institute of Applied Mathematics Delft University of Technology P.O. Box 5031 2600 GA Delft, The Netherlands
2 Institut für Analysis Karlsruhe Institute of Technology D-76128 Karlsruhe, Germany 
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Mark Veraar; Lutz Weis. Estimates for vector-valued holomorphic functions and Littlewood–Paley–Stein theory. Studia Mathematica, Tome 228 (2015) no. 1, pp. 73-99. doi: 10.4064/sm228-1-7

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