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Lorentz spaces with variable exponents
Author(s) -
Kempka Henning,
Vybíral Jan
Publication year - 2014
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.201200278
Subject(s) - mathematics , lorentz transformation , lp space , interpolation space , pure mathematics , variable (mathematics) , interpolation (computer graphics) , lorentz space , mathematical analysis , frame (networking) , banach space , functional analysis , classical mechanics , telecommunications , biochemistry , chemistry , physics , computer science , gene
We introduce Lorentz spacesL p ( · ) , q( R n )andL p ( · ) , q ( · )( R n )with variable exponents. We prove several basic properties of these spaces including embeddings and the identityL p ( · ) , p ( · )( R n ) = L p ( · )( R n ) . We also show that these spaces arise through real interpolation betweenL p ( · )( R n )andL ∞ ( R n ) . Furthermore, we answer in a negative way the question posed in [12][L. Diening, ] whether the Marcinkiewicz interpolation theorem holds in the frame of Lebesgue spaces with variable integrability.