The hardy and heisenberg inequalities in morrey spaces

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. © 2018 Australian Mathematical Publishing Association Inc.

Authors
Gunawan H.1 , Hakim D.I.2 , Nakai E.3 , Sawano Y. 2, 4
Journal
Bulletin of the Australian Mathematical Society
Publisher
Cambridge University Press
Number of issue
3
Language
English
Pages
480-491
Status
Published
Link
External link
DOI
10.1017/S0004972717001216
Volume
97
Year
2018
Organizations
  • 1 Department of Mathematics, Bandung Institute of Technology, Bandung, 40132, Indonesia
  • 2 Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami Ohsawa, Hachioji, Tokyo, 192-0397, Japan
  • 3 Department of Mathematics, Ibaraki University, Mito, Ibaraki, 310-8512, Japan
  • 4 RDUN, Peoples' Friendship University of Russia, Miklukho-Maklaya str. 6, Moscow, 117198, Russian Federation
Keywords
fractional power of Laplace operators; Hardy's inequality; Heisenberg's inequality; imaginary power of Laplace operators; interpolation inequality; Morrey spaces
Date of creation
19.10.2018
Date of change
19.10.2018
Short link
https://repository.rudn.ru/en/records/article/record/6634/
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Lyadov A.S., Maksimova Y.M., Shakhmatova A.S., Kirillov V.V., Parenago O.P.
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