Maximal functions associated with a set of directions

Abstract: There is a class of geometric problems in harmonic analysis associated with some curved manifolds such as the sphere or the paraboloid. In the study of these problems, relevant geometric maximal functions play a central role. In this talk, we consider maximal averaging operators along line segments oriented in a set of directions and their singular integral counterparts. How do operator norms of these maximal functions depend on the number and the distribution of directions? I will discuss some results in this direction and a divide-and-conquer approach for $L^2$ estimates.

analysis of PDEsclassical analysis and ODEsfunctional analysis

Audience: researchers in the topic

OARS Online Analysis Research Seminar

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