slideshow 3

Seminar on theory of function spaces

Linear and multilinear spherical maximal functions

Georgios Dosidis
University of Missouri, Columbia

 

Thursday, 8. October 2020 - 15:30 to 17:30

On-line seminar; for the access data write to Luboš Pick pick@karlin.mff.cuni.cz

 

The classical spherical maximal function is an analogue of the Hardy-Littlewood maximal function that involves averages over spheres instead of balls. We will review the classical bounds for the spherical maximal function obtained by Stein and explore their implications for partial differential equations and geometric measure theory. The main focus of this talk is to discuss recent results on the multilinear spherical maximal function and on a family of operators between the Hardy-Littlewood and the spherical maximal function. We will cover boundedness and convergence results for these operators for the optimal range of exponents. We will also include a discussion on Nikodym-type sets for spheres and spherical maximal translations.