A Hölder-type inequality on a regular rooted tree

Kenneth John Falconer

doi:10.1016/j.jmaa.2014.10.030

A Hölder-type inequality on a regular rooted tree

Kenneth John Falconer

Pure Mathematics

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2 Citations (Scopus)

3 Downloads (Pure)

Abstract

We establish an inequality which involves a non-negative function defined on the vertices of a finite m-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.

Original language	English
Pages (from-to)	913-923
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	423
Issue number	2
Early online date	16 Oct 2014
DOIs	https://doi.org/10.1016/j.jmaa.2014.10.030
Publication status	Published - 15 Mar 2015

Keywords

Hölder-type inequality
Rooted tree
Automorphism
Energy

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10.1016/j.jmaa.2014.10.030

FalconerJMAARevised
© 2014. Elsevier Ltd. All rights reserved. This is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications 16 October 2014 DOI 10.1016/j.jmaa.2014.10.030
Accepted author manuscript, 334 KB

http://arxiv.org/pdf/1410.6351.pdf

Cite this

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AB - We establish an inequality which involves a non-negative function defined on the vertices of a finite m-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.

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A Hölder-type inequality on a regular rooted tree

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