Optimal non-absolute domains and inequalities of Hardy operators

The topics of this thesis are two-folded. The first part considers the derivation of exact norms of a class of general operators acting between weighted ℓ∞-spaces, with possibly different weights in the domain and codomain, or of their restrictions to subcones of nonnegative or nonnegative monotone sequences. The results are applied to calculating exact norms for Cesàro and Copson operators, Cesàro and Copson operators minus identity, or to two-operators inequalities on ℓ∞-spaces, with powerweights. In the second part, we characterize the optimal non-absolute domain for the Hardy averaging operator minus identity, in all Lebesgue spaces. We also addressed the same problem for the dual Hardy operator minus identity.