Abstract
We investigate a convex function $\psi_{p,q,\lambda}=\max \{\psi_p, \lambda \psi_q \}$, $(1\leq q\lt p\leq \infty)$, and its corresponding absolute normalized norm $\| .\|_{\psi_{p,q,\lambda}}$. We determine a dual norm and use it for getting refinements of the classical Hölder inequality. Also, we consider a related concave function $\phi_{p,q,\lambda}=\min \{\psi_p, \lambda \psi_q \}$, $(0\lt p\lt q\leq 1)$.
Citation
Ludmila Nikolova. Sanja Varošanec. "Refinements of Hölder's inequality derived from functions $\psi_{p,q,\lambda}$and $\phi_{p,q,\lambda}$." Ann. Funct. Anal. 2 (1) 72 - 83, 2011. https://doi.org/10.15352/afa/1399900263
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