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Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces
Sihwaningrum I.a, Gunawan H.b, Nakai E.c
a Faculty of Mathematics and Natural Sciences, Jenderal Soedirman University, Purwokerto, 53122, Indonesia
b Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, 40132, Indonesia
c Department of Mathematics, Ibaraki University, Mito, 310-8512, Japan
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, WeinheimWe establish the boundedness and weak boundedness of the maximal operator and generalized fractional integral operators on generalized Morrey spaces over metric measure spaces (X,d,μ) without the assumption of the growth condition on μ. The results are generalization and improvement of some known results. We also give the vector-valued boundedness. Moreover we prove the independence of the choice of the parameter in the definition of generalized Morrey spaces by using the geometrically doubling condition in the sense of Hytönen.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]fractional integral operator,maximal operator,Morrey spaces,strong and weak boundedness[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text]The authors would like to thank Professor Sawano for his comments on the vector-valued boundedness. The authors would also like to thank the referees for their careful reading and many useful comments. The first author is supported by Fundamental Research Program, No. 2101/UN23.14/PN/2015, Directorate General of Higher Education, Indonesia. The second author is supported by The Research and Innovation Program, No. 107r/I1.C01/PL/2017, Bandung Institute of Technology. The third author is partially supported by Grant-in-Aid for Scientific Research (B), No. 15H03621, Japan Society for the Promotion of Science.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.1002/mana.201600350[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]