[NOVA Math] Seminar of Analysis


The Center of Mathematics and Applications (NOVA Math), promote the Seminar of Analysis with the title: “How the maximal operator's self-improving property translates into spaces of homogeneous type”.  Alina Shalukhina (NOVA FCT) is the speaker.


Abstract: We prove the self-improvement property of the Hardy–Littlewood maximal operator on quasi-Banach lattices with the Fatou property in the setting of spaces of homogeneous type—it is this accomplishment that is the focus and motive of the talk. Our result is a generalization of the boundedness criterion obtained in 2010 by Lerner and Ombrosi for maximal operators on quasi-Banach function spaces over Euclidean spaces. The specialty of the proof for spaces of homogeneous type lies in using adjacent grids of Hytönen–Kairema dyadic cubes and studying the maximal operator alongside its "dyadic" version; we will look into these technical curiosities in detail. Then we apply the obtained result to variable Lebesgue spaces over spaces of homogeneous type.


Wednesday, 19 June 2024, from 14:15 to 15:15.

Zoom: https://videoconf-colibri.zoom.us/j/93912858550?pwd=oiss4uahs9EiSqV52OwIsblRIZlGbs.1