报告题目：Multi-parameter Poincar\’e Inequality, Multi-parameter Carleson Embedding: Box Condition Versus Chang--Fefferman Condition
主 讲 人：Alexander Volberg 教授
ZOOM ID：975 2011 3597
Carleson embedding theorem is a building blocks for many singular integral operators and the main instrument in proving "Leibniz rule" for fractional derivatives (Kato--Ponce,Kenig). It is also an essential step in all known "corona theorems". Multi-parameter embedding is a tool to prove more complicated Leibniz rules that are also widely used in well-posedness questions for various PDEs. Alternatively, multi-parameter embedding appear naturally in questions of embedding of spaces of analytic functions in polydisc into Lebesgue spaces with respect to a measure in the polydisc. Carleson embedding theorems often serve as a first building block for interpolation in complex space and also for corona type results. The embedding of 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 1, 2, or 3. The main tool is the harmonic analysis on graphs with cycles. The answer is quite unexpected and seemingly goes against the well known difference between box and Chang--Fefferman condition that was given by Carleson quilts example of 1974. I will present results obtained jointly by Arcozzi, Holmes,Mozolyako,Psaromiligkos,Zorin-Kranich and myself.
Alexander “Sasha” L.Volberg, University Distinguished Professor of mathematics, specializes in harmonic analysis, singular integrals and operator theory and serves as the face of mathematics for MSU on a global scale. His 2014 paper in Acta Mathematica resolved the 30-year-old David-Semmes conjecture, concerning the possible structure of the singularity in the underlying measure of bounded Calderon-Zygmund operators.Volberg, who joined MSU in 1991, received his MS from St. Petersburg University, Russia, and his PhD from Steklov Mathematical Institute, Russian Academy of Science. Volberg has published more than 160 papers on his research. His many awards and honors include a Salem Prize, a Lars Onsager Medal for the Norwegian University of Science and Technology, and a Humboldt Foundation Professorship.Volberg was recently honored at an international conference in Bedlewo, Poland, that covered developments in the areas of analysis (notably, harmonic analysis, spectral theory of functions and operators, one-dimensional complex analysis, potential analysis, and their applications), in which Volberg has made substantial and recognized contributions over the past 25 years.