Der-Chen Chang: Hardy Spaces, Elliptic BVPs and Div-Curl Lemmas

The aim of this talk is threefold. First, we discuss Hardy spaces, $h^p_{\mathcal L} (\Omega)$, associated with an operator $\mathcal L$ which is a second order divergence form elliptic operator on $L2 (\Omega)$ with the Dirichlet or Neumann boundary condition for $0<p\le 1$.

Secondly, we establish regularity results for the Green operators in the context of Hardy spaces associated with these operators on a bounded semiconvex domain $\Omega\subset\R^n$ and div-curl lemmas.

Thirdly, we study relations between the Hardy spaces $h^p_r(\Omega)$ and $h^p_z(\Omega)$ which associated with standard Laplacian. This gives a new solution to the conjecture made by the speaker, S.G. Krantz and E.M.
Stein regarding the regularity of the Green operators for the Dirichlet and Neumann problems on $h^p_r(\Omega)$ and $h^p_z(\Omega)$ , respectively, for all $\frac{n}{n+1}<p\le 1$.