On new strengthened Hardy-Hilbert's inequality

Abstract

In this paper, a new inequality for the weight coefficient ω(q,n) in the form ω(q,n):=∑m=1∞1m+n(nm)1/q 1,1p+1q=1,n∈N) is proved. This is followed by a strengthened version ofthe Hardy-Hilbert inequality.

Keywords

• Hardy-Hilbert's inequality
• weight coefficient
• Holder's inequality.