A Hölder-type inequality on a regular rooted tree
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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.
Falconer , K J 2015 , ' A Hölder-type inequality on a regular rooted tree ' , Journal of Mathematical Analysis and Applications , vol. 423 , no. 2 , pp. 913-923 . https://doi.org/10.1016/j.jmaa.2014.10.030
Journal of Mathematical Analysis and Applications
© 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