Seminar

Analysis & Applications Seminar

Directional square functions

Speaker:  Luz Roncal (Basque Center for Applied Mathematics)
Date:  Friday, 09 April 2021 - 11:30
Place:  Online - zoom.us/j/96974398786

Abstract:
Charles Fefferman’s counterexample for the ball multiplier is intimately linked to square function estimates for directional singular integrals along all possible directions. Quantification of such a failure of the boundedness of the ball multiplier is measured, for instance, through Lp-bounds for the N-gon multiplier which provide information in terms of N. We present a general approach, developed in collaboration with N. Accomazzo, F. Di Plinio, P. Hagelstein, and I. Parissis, based on a directional embedding theorem for Carleson sequences, to study time-frequency model square functions associated to conical or directional Fourier multipliers. The estimates obtained for these square functions are applied to obtain sharp or quantified bounds for directional Rubio de Francia type square functions. In particular, a precise logarithmic bound for the polygon multiplier is shown, improving previous results.