Alexander Volberg (MSU)

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.