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Generalized fractional integrals on generalized Morrey spaces
Author(s) -
Nakai Eiichi
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.201200334
Subject(s) - mathematics , generalization , pure mathematics , maximal operator , operator (biology) , type (biology) , maximal function , variable (mathematics) , mathematical analysis , bounded function , ecology , biochemistry , chemistry , repressor , biology , transcription factor , gene
On generalized Morrey spaces with variable exponent p : R n → [ 1 , ∞ )and variable growth function φ : R n × ( 0 , ∞ ) → ( 0 , ∞ )the boundedness of generalized fractional integral operators I ρ is established, where ρ : R n × ( 0 , ∞ ) → ( 0 , ∞ ) . The result is a generalization of the theorems of Adams [1] (1975) and Gunawan [11] (2003). Moreover, we prove weak type boundedness. To do this we first prove the boundedness of the Hardy‐Littlewood maximal operator on the generalized Morrey spaces.