Heisenberg's inequality in $L^p$

TL;DR

This paper extends the classical Heisenberg uncertainty principle to Lebesgue spaces with power weights, providing new symmetric and non-symmetric versions of the inequality.

Contribution

It introduces novel versions of the Heisenberg-Pauli-Weyl uncertainty principle in weighted Lebesgue spaces, broadening its applicability.

Findings

Derived non-symmetric uncertainty inequalities

Established symmetric versions of the principle

Extended the principle to weighted Lebesgue spaces

Abstract

In this paper, we obtain non-symmetric and symmetric versions of the classical Heisenberg-Pauli-Weyl uncertainty principle in Lebesgue spaces with power weights.