Title: Harmonic Conjugation in Variable Exponent Harmonic Bergman Spaces Abstract: I will talk about the harmonic conjugation in variable harmonic Bergman space. In the first part of the talk, I'll provide an overview of the main result for constant exponent spaces.  Then I'll illustrate our latest research on the boundedness of harmonic conjugation in variable harmonic Bergman

Title: Regularity Estimates for PDE with Data in Non-Standard Spaces Abstract: In this talk I present recent joint work with D. Cruz-Uribe. Given a weak super-solution $u\in W^{1,2}_0(\Omega)$ of the elliptic equation $$-\textrm{Div}\left(Q(x)\nabla u(x) \right) = f(x)$$ in a smooth domain $\Omega$ of $\mathbb{R}^n$ with $f$ in the Birnbaum-Orlicz space $L^A(\Omega)$ ($A(t) = t^{n/2}\log^\sigma(e+t)$ with