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On Vector‐valued Inequalities of the Marcinkiewicz‐Zygmund, Herz and Krivine Type
Author(s) -
Gasch J.,
Maligranda L.
Publication year - 1994
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19941670106
Subject(s) - mathematics , extension (predicate logic) , pure mathematics , operator (biology) , type (biology) , simple (philosophy) , inequality , discrete mathematics , mathematical analysis , epistemology , computer science , ecology , biochemistry , chemistry , philosophy , repressor , biology , transcription factor , gene , programming language
Any continuous linear operator T: L p → L q has a natural vector‐valued extension T: L p ( l r n ) → L q ( l r n ) which is automatically continuous. Relations between the norms of these operators in the cases of p = q and r = 2 were considered by Marcinkiewicz ‐ Zygmund [28], Herz [14] and Krivine [19] ‐ [21]. In this paper we study systematically these relations and given some applications. It turns out that some known results can be proved in a simple way as a consequence of these developments.