Speaker: Alex Stokolos, Georgia Southern University
Title: On maximal operators associated to bases of some convex sets
Abstract: It will be shown that a differentiation basis associated to a dilation
and translation invariant basis of some multidimensional convex sets if
differentiate integral of any functioin from L^\infty must differentiate
integral of any function from L^p with some p<\infty. A quantitative version of
the statement along with the relation to the Nagel-Stein-Wainger,
Cordoba-Fefferman and Bateman theorems will be discussed. This is a joint result
with Paul Hagelstein.