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Zbl 1252.46016
Nikolova, Ludmila; Varošanec, Sanja
Refinements of Hölder's inequality derived from functions $\psi _{p,q,\lambda }$ and $\varphi _{ p,q,\lambda }$. (English)
[J] Ann. Funct. Anal. AFA 2, No. 1, 72-83, electronic only (2011). ISSN 2008-8752/e

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 $\varphi_{ p,q,\lambda} = \min\{\psi_p, \lambda \psi_q\}\ (0 < p < q \leq 1$).

MSC 2000:: *46B99 Normed linear spaces and Banach spaces
26D15 Inequalities for sums, series and integrals of real functions

Keywords: Hölder's inequality; absolute normalized norm; concave function

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Zentralblatt MATH Berlin [Germany]