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Complex interpolation of various subspaces of Morrey spaces

Hakim D.I.a,b, Sawano Y.a,c

a Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Tokyo, 192-0397, Japan
b Department of Mathematics, Bandung Institute of Technology, Bandung, 40132, Indonesia
c Department of Mathematics Analysis and the Theory of Functions, Peoples’ Friendship University of Russia, Moscow, 117198, Russian Federation

[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]© 2020, Science China Press and Springer-Verlag GmbH Germany, part of Springer Nature.In this article, we discuss the complex interpolation of various closed subspaces of Morrey spaces. We have been considering some closed subspaces of Morrey spaces in our earlier works. The main property that we need is the lattice property but in connection with the diamond spaces defined by Yuan et al. (2015), it seems to be natural to consider the convolution property as well. Our result will extend the results by Hakim and Sawano (2017) and Hakim et al. (2017).[/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]42B35,46870,46B26,complex interpolation,smoothness Morrey spaces,square function[/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 second author was supported by Grant-in-Aid for Scientific Research (C) (Grant No. 16K05209), Japan Society for the Promotion of Science and Department of Mathematics Analysis and the Theory of Functions, Peoples’ Friendship University of Russia. The authors thank the referees for their useful comments.[/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/10.1007/s11425-017-9318-0[/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]