Hi! I am Fernando Ballesta Yagüe, a PhD candidate at Universidad Complutense de Madrid (UCM), Spain, under the supervision of María Jesús Carro.
This webpage is work in progress. For the moment, you can find here a description of my research and my publications so far.
My area of research is Harmonic Analysis.
More specifically, my thesis is focused on the study of boundary value problems for the Laplace equation on graph Lipschitz domains in the plane with rough data, using weighted theory as the main tool. The idea is that this equation is preserved under the composition with a conformal mapping. Hence, the problem can be taken to the upper half plane, where a explicit solution is known. There, weighted estimates appear due to the jacobian of the change of variables, and therefore the partial differential equation is reduced to a problem in weighted theory.
I have also worked on Sparse Domination, a very useful technique in weighted theory.
Besides, I am broadly interested in learning about other topics in Harmonic Analysis and their relation to other branches of Mathematics. For example, I have worked on a problem coming from Several Complex Variables, and I am starting to learn about oscillatory integral operators in more depth.