# 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

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

The following have contributed to this page: Hendra Gunawan

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