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THE HARDY AND HEISENBERG INEQUALITIES IN MORREY SPACES

  • HENDRA GUNAWAN (a1), DENNY IVANAL HAKIM (a2), EIICHI NAKAI (a3) and YOSHIHIRO SAWANO (a4) (a5)
Abstract

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.

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hgunawan@math.itb.ac.id
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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.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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