$L^p$ Hardy‎ -‎Rellich and uncertainty principle inequalities on the sphere

Document Type: Original Article


1 ‎‎‎Department of Physical Sciences‎ ‎Landmark University‎, ‎P‎. ‎M‎. ‎B‎. ‎1001‎, ‎Omu-Aran‎, ‎Kwara State‎, ‎Nigeria

2 Department of Mathematics and Statistics, Osun State College of Technology, P. M. B. 1011, Nigeria


‎In this paper, we study the Hardy-Rellich type inequalities and uncertainty principle on the geodesic sphere‎. ‎Firstly‎, ‎we derive $L^p$-Hardy inequalities via divergence theorem‎, ‎which are in turn used to establish the $L^p$ Rellich inequalities‎. ‎We also establish Heisenberg uncertainty principle on the sphere via the Hardy-Rellich type inequalities‎. ‎The best constants appearing in the inequalities are shown to be sharp‎.