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.
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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
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).
Hendra Gunawan
Institut Teknologi Bandung
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This page is a summary of: THE HARDY AND HEISENBERG INEQUALITIES IN MORREY SPACES, Bulletin of the Australian Mathematical Society, March 2018, Cambridge University Press,
DOI: 10.1017/s0004972717001216.
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