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One‐Sided BMO Spaces
Author(s) -
MartínReyes F. J.,
De La Torre A.
Publication year - 1994
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/49.3.529
Subject(s) - mathematics , maximal function , combinatorics , physics , mathematical analysis
In this paper we introduce the one‐sided sharp functions denned byf + ♯ ( x ) = sup h > 01 h∫ x x + h( f ( y ) − 1 h∫ x + h x + 2 hf ) + d y , andf − ♯ ( x ) = sup h > 01 h∫ x − h x( f ( y ) − 1 h∫ x − 2 h x − hf ) + d y , where z + = max( z , 0). We study the BMO spaces associated tof + ♯andf − ♯and their relation with the good weights for the one‐sided Hardy‐Littlewood maximal functions. Finally, as an application of our results, we characterize the weights for one‐sided fractional integrals and one‐sided fractional maximal operators.