Семинар за анализу, 20. октобар 2022.

• 14. Октобар, 2022
• Коментари (0)

Наредни састанак Семинара биће одржан онлајн у четвртак, 20. октобра 2022, са почетком у 19 часова.

Предавач: Alexander Volberg

Наслов предавања: DYADIC RECTANGLES OR DO WE KNOW THE CARLESON EMBEDDING ON BI-DISC?

Апстракт:
Carleson embedding theorem often serves as a first building block for interpolation in complex domain, for the theory of Hankel operators, and also in PDE. Its other name is paraproducts estimates. The embedding of certain spaces of holomorphic functions on n-polydisc can be reduced (without loss of information) to the boundedness of weighted multi-parameter dyadic Carleson embedding. We find the necessary and sufficient condition for this Carleson embedding in n-parameter case, when n is  2, or 3 (for n=1 all was known). The main tool is the harmonic analysis on graphs with cycles. The answer is quite unexpected and seemingly (only seemingly) goes against  Carleson quilts counterexample. The main tool is an unexpected combinatorial properties of positive measures on cube in dimensions 2, 3. I will present results obtained jointly by Arcozzi, Holmes, Mozolyako, Psaromiligkos, Zorin-Kranich and myself. But spaces of holomorphic functions in bi-disc mentioned above do not include the classical Hardy space on bi-disc. Why we do not know the embedding theorem for Hardy space on bi-disc? There is a deep reason for that, which will be explained.

Линк за приступ предавању:
https://us02web.zoom.us/j/6636215428?pwd=bllJSTUvZ0E5MjhkMkxYa3RYYzZpQT09
Meeting ID: 663 621 5428
Passcode: 7h6KR1