TY - JOUR

T1 - Some properties related to trace inequalities for the multi-parameter Hardy operators on poly-trees

AU - Arcozzi, Nicola

AU - Mozolyako, Pavel

AU - Perfekt, Karl Mikael

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85069491106&partnerID=8YFLogxK

U2 - 10.1007/s13324-019-00327-5

DO - 10.1007/s13324-019-00327-5

M3 - Article

AN - SCOPUS:85069491106

VL - 9

SP - 937

EP - 954

JO - Analysis and Mathematical Physics

JF - Analysis and Mathematical Physics

SN - 1664-2368

IS - 3

ER -