Another approach to weighted inequalities for a superposition of Copson and Hardy operators

Abstract

In this paper, we present a solution to the inequality $$\left({\int }_0^{\infty }\right({\int }_x^{\infty }({\int }_0^{t}h{)}^{q}w(t)dt{)}^{r/q}u(x)ds{)}^{1/r}\le C({\int }_0^{\infty }{h}^{p}v{)}^{1/p},h\in {\mathfrak{M}}^{+}(0,\infty ),$$ using a combination of reduction techniques and discretization. Here $1\le p<\infty$, $0<q,r<\infty$ and $u,v,w$ are weight functions on $(0,\infty )$.

13 pages