Some properties related to trace inequalities for the multi-parameter Hardy operators on poly-trees

2018/11/02 by Arcozzi, Nicola, Mozolyako, Pavel, Perfekt, Karl-Mikael
#31B15 #31B30 #32A37 #42B25 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1811.01036

Abstract

In this note we investigate the multi-parameter Potential Theory on the weighted d-tree (Cartesian product of several copies of uniform dyadic tree), which is connected to the discrete models of weighted Dirichlet spaces on the polydisc. We establish some basic properties of the respective potentials, capacities and equilibrium measures (in particular in the case of product polynomial weights). We explore multi-parameter Hardy inequality and its trace measures, and discuss some open problems of potential-theoretic and combinatorial nature.

Related

• Weighted discrete Hardy inequalities on trees and applications
• Bellman function for Hardy's inequality over dyadic trees
• Hardy-Littlewood inequalities for multipolynomials
• The space of Hardy-weights for quasilinear operators on discrete graphs
• Carleson embedding on tri-tree and on tri-disc