My research interests is complex analysis. More specifically speaking, I work on the interactions between theory of spaces of analytic functions and operator theory. I am mainly interested in the following topics:
-Hardy spaces, Bergman spaces, BMOA, Bloch functions, Q_p spaces, normal functions, spaces of Dirichlet type.
-Univalent functions and function spaces.
-Planar domains as images of the disc under conformal mappings. Schwarzian derivative.
-Inner functions: Factorization theorems, intregability ot he derivative of an inner function. Behaviour
as improving multipliers.
-Embedding theorems: Carleson measures, Hausdorff capacities and potential theory. Measures on trees.
-Distribution of zeros, uniqueness sets, interpolating and sampling sequences in spaces of analytic functions. Uniformly discrete sequences, interpolation sequences.
- Multiplication operators, integration operators, Toeplitz operators, Hankel operators (Hilbert matrices) and projections.
- Spectral theory.
-Weighted inequalities, A_\infty weights....