A H\"older-type inequality on a regular rooted tree
Classical Analysis and ODEs
2014-10-24 v1
Abstract
We establish an inequality which involves a non-negative function defined on the vertices of a finite -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, H\"{o}lder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.
Keywords
Cite
@article{arxiv.1410.6351,
title = {A H\"older-type inequality on a regular rooted tree},
author = {Kenneth J Falconer},
journal= {arXiv preprint arXiv:1410.6351},
year = {2014}
}