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Parametrized Littlewood–Paley operators on Hardy and weak Hardy spaces
Author(s) -
Ding Yong,
Lu Shanzhen,
Xue Qingying
Publication year - 2007
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.200410487
Subject(s) - mathematics , hardy space , type (biology) , lambda , pure mathematics , extension (predicate logic) , function (biology) , combinatorics , physics , ecology , evolutionary biology , computer science , optics , biology , programming language
In this paper, we give the boundedness of the parametrized Littlewood–Paley function $ \mu ^{*,\rho}_{\lambda} $ on the Hardy spaces and weak Hardy spaces. As the corollaries of the above results, we prove that $ \mu ^{*,\rho}_{\lambda} $ is of weak type (1, 1) and of type ( p , p ) for 1 < p < 2, respectively. This results are substantial improvement and extension of some known results. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)