TY - JOUR
T1 - Riesz type potential operators in generalized grand Morrey spaces
AU - Kokilashvili, Vakhtang
AU - Meskhi, Alexander
AU - Rafeiro, Humberto
N1 - Funding Information:
The first and second author were partially supported by the Shota Rustaveli National Science Foundation Grant (Contract No. D/13-23). The third author was partially supported by FCT Fundação para a Ciência e a Tecnologia (Grant SFRH/BPD/63085/2009), Portugal and by Pontificia Univer-sidad Javeriana under the research project ID 5453.
PY - 2013/3/1
Y1 - 2013/3/1
N2 - 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 operators. The boundedness of Riesz type potential operators is also obtained in the framework of homogeneous and also in the nonhomogeneous cases in generalized grand Morrey spaces.
AB - 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 operators. The boundedness of Riesz type potential operators is also obtained in the framework of homogeneous and also in the nonhomogeneous cases in generalized grand Morrey spaces.
KW - Calderón-Zygmund operator
KW - Hardy-Littlewood maximal operator
KW - Morrey spaces
KW - potentials
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U2 - 10.1515/gmj-2013-0009
DO - 10.1515/gmj-2013-0009
M3 - Article
AN - SCOPUS:84875503336
SN - 1572-9176
VL - 20
SP - 43
EP - 64
JO - Georgian Mathematical Journal
JF - Georgian Mathematical Journal
IS - 1
ER -