Hardy inequalities for functions vanishing at negligible sets and its applications

Abstract

Hardy inequalities for smooth functions vanishing at a negligible set in contained in 0 is considered. The result gives best constants of these inequalities, which depends on the structure of the corresponding negligible set. As applications, related Schrödinger operators are also considered.

Keywords:

• Hardy inequalities
• spherical harmonics
• Friedrichs’ extension

AMS Subject Classifications:

• Primary: 35A23
• Secondary: 47B25

Notes

S. Watanabe is supported in part by the JSPS Grant-in-Aid for Scientific Research (C) 24540112.