Nikolova, Ludmila; Varošanec, Sanja Refinements of Hölder’s inequality derived from functions \(\psi _{p,q,\lambda }\) and \(\varphi _{ p,q,\lambda }\). (English) Zbl 1252.46016 Ann. Funct. Anal. 2, No. 1, 72-83 (2011). Summary: 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 \(\| . \|_{\psi_{p,q,\lambda}} \). We determine a dual norm and use it for getting refinements of the classical Hölder inequality. Also, we consider a related concave function \(\varphi_{ p,q,\lambda} = \min\{\psi_p, \lambda \psi_q\}\;(0 < p < q \leq 1\)). Cited in 3 Documents MSC: 46B99 Normed linear spaces and Banach spaces; Banach lattices 26D15 Inequalities for sums, series and integrals Keywords:Hölder’s inequality; absolute normalized norm; concave function PDFBibTeX XMLCite \textit{L. Nikolova} and \textit{S. Varošanec}, Ann. Funct. Anal. 2, No. 1, 72--83 (2011; Zbl 1252.46016) Full Text: DOI EMIS