FMVE160 Maximal functions and convergence

Kursens poäng (högskolepoäng, hp) 6 hp
Kursen ges normalt Only once
Tillhör forskarskola
Tillhör institution Matematiska vetenskaper
Kursansvarig
peters@math.chalmers.se
Kursbeskrivning
Poisson integrals and many other operators are defined via integration of a function against an integral kernel. One can often recover the values of the function as limits of the integral at some kind of boundary. This usually works well when the function is continuous. To prove that it works also for more general functions, like L^p functions, one is inevitably led to a maximal function, obtained essentially by replacing "lim" by "sup". One then has to control the size of this maximal function. The course will discuss several settings of this kind, including multiple Poisson integrals.

Publicerad: ti 29 jan 2013. Ändrad: ti 08 jan 2019