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Zbl 1157.26009
Perić, I.
Mixed means for centered and uncentered averaging operators over spheres and related results.
(English)
[J] Banach J. Math. Anal. 2, No. 2, 150-162, electronic only (2008). ISSN 1735-8787/e

The author derives and discusses the mixed-mean inequalities for integral power means over centred and uncentred spheres. In addition, the associated Hardy-type inequalities corresponding to the operators ${\cal S}^{c}_{\delta,\alpha}$ and ${\cal S}^{\text{unc}}_{\delta,\alpha}$ defined on the collection of centred and uncentred spheres are equally derived.
MSC 2000:
*26D10 Inequalities involving derivatives, diff. and integral operators
26D15 Inequalities for sums, series and integrals of real functions

Keywords: Mixed means; integral power mean; power weights; centred and uncentred spheres; polar coordinates; Hardy's inequality; Carleman's inequality; spherical maximal functions; lower bounds for operator norms

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