2012/04/10 by Kokilashvili, Vakhtang, Meskhi, Alexander, Rafeiro, Humberto
#42B20 #42B25 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.1204.2208
In this paper we introduce generalized grand Morrey spaces in the framework of quasimetric measure spaces, in the spirit of the so-called grand Lebesgue spaces. We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in generalized grand Morrey spaces to the corresponding boundedness in Morrey spaces, as a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator as well as the boundedness of Calderón-Zygmund potential type operators. Boundedness of Riesz type potential operators are also obtained in the framework of homogeneous and also in the nonhomogeneous case in generalized grand Morrey spaces.