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.
Arcozzi N., Mozolyako P., Perfekt K.-M. (2019). Some properties related to trace inequalities for the multi-parameter Hardy operators on poly-trees. ANALYSIS AND MATHEMATICAL PHYSICS, 9(3), 937-954 [10.1007/s13324-019-00327-5].
Some properties related to trace inequalities for the multi-parameter Hardy operators on poly-trees
Arcozzi N.;Mozolyako P.;
2019
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
