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

2015/06/26 by Mark Veraar, Veraar, Mark, Lutz Weis +1
Mathematics · #46B20 #46B70 #46E40 #47D07 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46B09 #Secondary: 42B25 #math.FA #msc:42B25 #msc:46B09 #msc:46B20 #msc:46B70 #msc:46E40 #msc:47D07

paper · pdf · doi:10.48550/arxiv.1506.08013

Accepted for publication in Studia Mathematica

arxiv created 2015/09/28 · arxiv updated 2015/09/29

Abstract

In this paper 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 for 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.

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