THE HARDY AND HEISENBERG INEQUALITIES IN MORREY SPACES

HENDRA GUNAWAN, DENNY IVANAL HAKIM, EIICHI NAKAI, YOSHIHIRO SAWANO
  • Bulletin of the Australian Mathematical Society, March 2018, Cambridge University Press
  • DOI: 10.1017/s0004972717001216

THE HARDY AND HEISENBERG INEQUALITIES IN MORREY SPACES

What is it about?

[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 space.

Why is it important?

Heisenberg's inequality is one of the most important inequality in mathematics as well as in physics. The original inequality was proved in L^2 spaces, and then extended to L^p spaces. In this paper, we prove that the inequality also holds in Morrey spaces.

Perspectives

Hendra Gunawan (Author)
Institut Teknologi Bandung

I proved an inequality for the imaginary powers of the Laplacian about 15 years ago and I began to study about Morrey spaces at the same time, without any expectation that the two topics would intertwine -- until I read the paper by M. Cowling, P. Ciatti, and F. Ricci (2015).

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http://dx.doi.org/10.1017/s0004972717001216

The following have contributed to this page: Hendra Gunawan