Seminario Análisis y Aplicaciones
Directional square functions
Ponente: Luz Roncal (Basque Center for Applied Mathematics)Fecha: viernes 09 de abril de 2021 - 11:30Lugar: Online - zoom.us/j/96974398786
Resumen:
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.