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

Arcozzi, N., Mozolyako, P. and 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). pp. 937-954. ISSN 1664-235X doi: 10.1007/s13324-019-00327-5

Abstract/Summary

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.

Item Type	Article
URI	https://reading-clone.eprints-hosting.org/id/eprint/83791
Identification Number/DOI	10.1007/s13324-019-00327-5
Refereed	Yes
Divisions	Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
Publisher	Springer
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