Lisbon Webinar in Analysis and Differential Equations

The helical maximal function

Sala P3.10, Instituto Superior Técnico (com transmissão via Zoom)

Por David Beltran (Universitat de València).

Consider the maximal function associated with averages over dilates of the helix (or, more generally, of any curve with non-vanishing curvature and torsion). This object can be seen as a 3-dimensional analogue of the classical circular maximal function in the plane, studied by Bourgain (sharp $L^p$ bounds for $p>2$) and Schlag and Schlag-Sogge (sharp $L^p$-$L^q$ bounds). In this talk, we report sharp 3-dimensional versions of those well-known 2-dimensional results, which use recent developments in multilinear harmonic analysis. This is based on joint works with Shaoming Guo, Jonathan Hickman and Andreas Seeger ($L^p$ bounds), and Jennifer Duncan and Jonathan Hickman ($L^p$-$L^q$ bounds).

Transmissão via Zoom (pw: lisbonwade).

The Lisbon Webinar in Analysis in Differential Equations is a joint iniciative of CAMGSD, CMAFcIO and GFM, three research centers of the University of Lisbon. It is aimed at filling the absence of face-to-face seminars and wishes to be a meeting point of mathematicians working in the field.