engleski

Refinements of Hölder's inequality derived from functions ψp,q,λand ϕp,q,λ

We investigate a convex function $\psi_{; ; p, q, \lambda}; ; =max {; ; \psi_p, \lambda \psi_q}; ; $ $(1\leq q, p\leq \infty)$ and its corresponding absolute normalized norm $\| . \|_{; ; p, q, \lambda}; ; $. We determine a dual norm and use it for getting refinements of the classical H\" older inequality. Also, we consider a related concave function $\phi_{; ; p, q, \lambda}; ; =min {; ; \psi_p, \lambda \psi_q}; ; $, $(p, q\in (0, 1)$.

Holder's inequality ; absolute normalized norm ; concave function ; $\psi_{; ; p ; q ; \lambda}; ; $ function

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