Lorentz–Shimogaki and Boyd theorems for weighted Lorentz spaces | Zendy

Agora Elona | Zendy; Antezana Jorge | Zendy; Carro María J. | Zendy; Soria Javier | Zendy

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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 ) .

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