We derive whole series of new integral
inequalities of the Hardy-type, with non-conjugate exponents.
First, we prove and discuss two equivalent general
inequa-li-ties of such type, as well as their corresponding
reverse inequalities. General results are then applied to special
Hardy-type kernel and power weights. Also, some estimates of
weight functions and constant factors are obtained. In
particular, we obtain generalizations and improvements of some
recent results, in the literature.