A Hölder-type inequality on a regular rooted tree
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.
Citation
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
Publication
Journal of Mathematical Analysis and Applications
Status
Peer reviewed
ISSN
0022-247XType
Journal article
Collections
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