Premium
Some new characterizations on spaces of functions with bounded mean oscillation
Author(s) -
Yang Dachun,
Zhou Yuan
Publication year - 2010
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.200610823
Subject(s) - bounded mean oscillation , mathematics , type (biology) , bounded function , equivalence (formal languages) , homogeneous , pure mathematics , space (punctuation) , oscillation (cell signaling) , maximal function , assertion , mathematical analysis , hardy space , discrete mathematics , combinatorics , computer science , ecology , genetics , biology , programming language , operating system
Let X be a space of homogeneous type. The authors introduce some generalized approximations to the identity (for short, GAI) with optimal decay conditions in the sense that these conditions are the sufficient and necessary conditions for these GAI's to characterize BMO( X ), the space of functions with bounded mean oscillation on X . The authors also obtain a new John‐Nirenberg‐type inequality associated with GAI's, which leads some new characterizations of BMO( X ) in terms of rearrangement functions, and certain maximal functions related to GAI's. Some variants of these characterizations for BMO‐type spaces on X of Duong and Yan are also established. Moreover, the equivalence between BMO and the space of BMO type on Ahlfors n ‐regular quasimetric measure spaces is obtained, which confirms an assertion of Duong and Yan (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)