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

  • Nicola ArcozziEmail author
  • Pavel Mozolyako
  • Karl-Mikael Perfekt
Article
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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.

Mathematics Subject Classification

31B15 31B30 32A37 42B25 

Notes

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Università di BolognaBolognaItaly
  2. 2.Department of Mathematics and StatisticsUniversity of ReadingReadingUnited Kingdom

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