SHARP CONFORMALLY INVARIANT HARDY-TYPE INEQUALITIES WITH REMAINDERS

In the present paper we establish new Hardy-Maz'ya-type inequalities with remainders for all continuously differentiable functions with compact support in the half space R. The weight functions depend on the distance to the boundary or on the distance to the origin. Also new sharp Avkhadiev-Hardy-type inequalities involving the distance to the boundary or the hyperbolic radius are proved. We consider Avkhadiev-Hardy-type inequalities in simply and doubly connected plain domains and in tube-domains.