Bekarys Bekmaganbetov will give a talk at 2/28/2023.

The Fefferman-Stein inequality is an important tool in obtaining a priori estimates and solvability for elliptic and parabolic equations, perhaps with rough coefficients. In this talk we will discuss a generalized version of the Fefferman-Stein inequality. The underlying space is the so-called homogeneous type space, i.e. equipped with a quasi-metric and a doubling measure, and $A_p$ weights are also considered. Such generalization is used in proving solvability of elliptic and parabolic equations with mixed norms and weights.