Visit of Professor Pavel Mozolyako

November-December 2022- Professor Pavel Mozolyako is hosted by Evgueni Abakoumov (LAMA/UGE) for one month to collaborate with him on a joint scientific research on “Potential theory on graphs and weighted Hardy operator”.

A colloquium will take place on Tuesday, November 15, 2022, in Université Gustave Eiffel Copernic Building 4th floor room 4B125

10:30-11:00: welcome coffee
11:00-12:00: seminar talk by Pavel Mozolyako (Saint-Petersburg State University, Faculty of Mathematics and Computer Science, Russia).

Title: Potential theory on graphs and weighted Hardy operator.

Abstract: Let Γ be a finite rooted directed graph without directed cycles, i.e. a finite partially ordered set with a unique maximal element. We introduce a Potential Theory on such graphs via a weighted Hardy operator I(w) and discuss some of its basic properties – energy, capacity, equilibrium measures and such. Our local aim is to investigate the boundedness of I(w) as a two-weighted L2-embedding, which is, in turn, connected to several classical problems, for example the description of Carleson measures for different spaces of analytic and/or holomorphic functions on the disc/polydisc; weighted integration operators in (R+)^n; L2-boundedness of the rectangular maximal functions etc. We plan to give a short review of known results and (very briefly) discuss some of the aforementioned connections and applications.

Talk based on a joint work with N. Arcozzi, A. Volberg and P. Zorin-Kranich.