Title: Solvability of the Dirichlet Problem with L^p Data for Caloric Measure Abstract: This talk concerns two probability measures. First, we consider harmonic measure, which gives solutions to the Dirichlet problem associated to Laplace's equation. Additionally, we may view harmonic measure as the “hitting probability" for Brownian motion. This probabilistic interpretation shows the connection between

Title: Non-homogeneous T(1) theorem for singular integrals on product quasimetric spaces Abstract: In the Calderón-Zygmund Theory of Singular Integrals, the T(1) theorem of David and Journé is one of the most celebrated theorems. It gives easily-checked criteria for a singular integral operator T to be bounded from L^2(R^n) to L^2(R^n), meaning T(f) is bounded for

Title: Novel Bellman Estimates for Ap Weights Abstract: The Bellman function method is an assortment of tools for obtaining sharp inequalities in harmonic analysis. To handle an inequality, one fixes a set of parameters, called Bellman variables, and maximizes (or minimizes) the left-hand side subject to these constraints. The solution of the corresponding extremal problem