# Young Women in Harmonic Analysis and PDE

## December 2-4, 2016

### Cruz Prisuelos (ICMAT)

#### Weighted Hardy spaces associated with operators

In this talk we consider weighted Hardy spaces defined using conical square functions, non-tangential maximal functions, and the Riesz transform associated with an elliptic operator in divergence form $L$. In the case of conical square functions and non-tangential maximal functions, for $0 < p\leq 1$, we give a molecular characterization of them, and for $p\in \mathcal{W}_w(p_-(L),p_+(L))$, we show that they are isomorphic to the $L^p(w)$ spaces. Besides in the case of the Riesz transform we show that the corresponding weighted Hardy space is isomorphic to the weighted Hardy space defined by a particular conical square function.