A Hölder-type inequality on a regular rooted tree

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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 languageEnglish
Pages (from-to)913-923
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume423
Issue number2
Early online date16 Oct 2014
DOIs
Publication statusPublished - 15 Mar 2015

Keywords

  • Hölder-type inequality
  • Rooted tree
  • Automorphism
  • Energy

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