One dimensional Weighted Hardy's Inequalities and application

Abstract

In the present paper we shall improve one dimensional weighted Hardy inequalities with one-sided boundary condition by adding sharp remainders. As an application, we shall establish n dimensional weighted Hardy inequalities in a bounded smooth domain with weight functions being powers of the distance function d(x) to the boundary. Our results will be applicable to variational problems in a coming paper.

16 pages. This research was partially supported by Grant-in-Aid for Scientific Research (No. 16K05189) and (No. 15H03621)