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The hardy and heisenberg inequalities in morrey spaces
Gunawan H.a, Hakim D.I.b, Nakai E.c, Sawano Y.b,d
a Department of Mathematics, Bandung Institute of Technology, Bandung, 40132, Indonesia
b Department of Mathematics and Information Sciences, Tokyo Metropolitan University, Hachioji, Tokyo, 192-0397, Japan
c Department of Mathematics, Ibaraki University, Mito, Ibaraki, 310-8512, Japan
d RDUN, 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]© 2018 Australian Mathematical Publishing Association Inc.We use the Morrey norm estimate for the imaginary power of the Laplacian to prove an interpolation inequality for the fractional power of the Laplacian on Morrey spaces. We then prove a Hardy-type inequality and use it together with the interpolation inequality to obtain a Heisenberg-type inequality in Morrey spaces.[/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 power of Laplace operators,Hardy’s inequality,Heisenberg’s inequality,imaginary power of Laplace operators,interpolation inequality,Morrey spaces[/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 first author was supported by the ITB Research and Innovation Program 2017. The second and third authors were supported by a Grant-in-Aid for Scientific Research (B) No. 15H03621, Japan Society for the Promotion of Science. The fourth author is supported by a Grant-in-Aid for Scientific Research (C) No. 16K05209, Japan Society for the Promotion of Science, and Peoples’ Friendship University of Russia. ©c 2018 Australian Mathematical Publishing Association Inc.[/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/10.1017/S0004972717001216[/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]