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

Mark Veraar; Lutz Weis

Mark Veraar ; Lutz Weis

Studia Mathematica, Tome 231 (2015), p. 73-99 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $L^{p} (X) \subseteq γ (X) \subseteq L^{q} (X)$ , 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.

Publié le : 2015-01-01

Zbl 06497981

EUDML-ID : urn:eudml:doc:285377

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     title = {Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory},
     journal = {Studia Mathematica},
     volume = {231},
     year = {2015},
     pages = {73-99},
     zbl = {06497981},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-1-7}
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Mark Veraar; Lutz Weis. Estimates for vector-valued holomorphic functions and Littlewood-Paley-Stein theory. Studia Mathematica, Tome 231 (2015) pp. 73-99. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm228-1-7/