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Mathematical Colloquium of the Bauman Moscow State Technical University
May 28, 2020 17:30, Moscow, This talk will be organized as Zoom video-meeting
 


Hardy inequality on the tree and bi-tree and some (unexpected) combinatorial properties of planar measures

P. A. Mozolyako

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Abstract: We consider embeddings of various spaces of analytic functions in polydisc into Lebesgue spaces with respect to a measure in the polydisc. These problems can be often moved to a discrete setting, by considering weighted Dirichlet spaces on (poly-) trees and weighted dyadic multi-parameter Hardy operator. We find the necessary and sufficient condition for this operator to be bounded in n-parameter case, when n is 1, 2, or 3. The answer is quite unexpected—it is a certain combinatorial property of all measures in dimension 2 and 3 — and seemingly goes against the well known difference between box and Chang–Fefferman condition that was given by Carleson quilts example of 1974.

Zoom-conference identificator: 817 8038 8576; Password: 453751

Website: https://us02web.zoom.us/j/81780388576?pwd=dS92dlRFZkdLcHZmVzRVZHVZSGVzQT09
 
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