Dimension-free maximal and r-variational Lp-estimates of averaging operators for products of Euclidean balls and spheres

In this thesis, we will provide new dimension-free L^p-bounds for the centered maximal function for products of Euclidean balls and for the r-variations of the underlying averaging operators. We also provide similar new results for products of spheres.

In dieser Arbeit liefern wir neue dimensionsunabhängige L^p-Schranken für die zentrierte Maximalfunktion bzgl. Produkten euklidischer Kugeln sowie für die r-Variationen der zugrundeliegenden Mittelungsoperatoren. Wir liefern zudem ähnliche neue Resultate für Produkte von Sphären.


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