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Lorentz–Shimogaki and Boyd theorems for weighted Lorentz spaces
Author(s) -
Agora Elona,
Antezana Jorge,
Carro María J.,
Soria Javier
Publication year - 2014
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/jdt063
Subject(s) - lorentz transformation , mathematics , lorentz space , characterization (materials science) , pure mathematics , hardy space , operator (biology) , type (biology) , maximal operator , mathematical physics , mathematical analysis , physics , bounded function , classical mechanics , ecology , biochemistry , chemistry , repressor , biology , transcription factor , optics , gene
We prove the Lorentz–Shimogaki and Boyd theorems for the spacesΛ u p ( w ) . As a consequence, we give the complete characterization of the strong boundedness of H on these spaces in terms of some geometric conditions on the weights u and w , whenever p >1. For these values of p , we also give the complete solution of the weak‐type boundedness of the Hardy–Littlewood operator onΛ u p ( w ) .