The APDE seminar on
Monday, 01/13 Monday, 01/27 will be given by Alexander Volberg in Evans 939 from 4:10 to 5pm.
Title: Box condition versus Chang–Fefferman condition for weighted multi-parameter paraproducts.
Abstract: Paraproducts are building blocks of many singular integral operators and the main instrument in proving “Leibniz rule” for fractional derivatives (Kato–Ponce). Also multi-parameter paraproducts appear naturally in questions of embedding of spaces of analytic functions in polydisc into Lebesgues spaces with respect to a measure in the polydisc. The latter problem (without loss of information) can be often reduced to boundedness of weighted dyadic multi-parameter paraproducts. We find the necessary and sufficient condition for this boundedness in n-parameter case, when n is 1, 2, or 3. 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.