I obtained my PhD degree in 2021 at the TU Delft with my dissertation Sharp Estimates and Extrapolation for Multilinear Weight Classes.

My current main research interests are: 

• Singular integrals in Banach function spaces. While singular integrals in the setting of weighted Lebesgue spaces are well-understood, this is not always the right setting for every problem: many PDEs have initial data belonging to different classes of spaces, such as weighted variable Lebesgue and weighted Morrey spaces. Unlike in weighted Lebesgue spaces, in these settings the Muckenhoupt condition is no longer equivalent to the boundedness of singular integrals. A main goal of my research is to develop and understand alternative criteria to the Muckenhoupt condition through the study of classical Calderón-Zygmund theory in the setting of Banach function spaces.

• Singular integrals in weighted Lebesgue spaces. Many singular integrals are not bounded for the full range of exponents, but rather for a limited range. This typically occurs when the singular integral is associated to some form of non-smoothness, such as a Riesz transform on a rough domain, or a Riesz transform associated to an elliptic operator with rough coefficients. Moreover,  important multilinear singular integrals in time-frequency analysis such as the bilinear Hilbert transform, and in geometric measure theory such as the bilinear spherical maximal operator, can also be understood in limited range settings. One of my main goals is to understand the weighted behavior of these objects in both the strong-type and the weak-type setting.

• Vector-valued extensions of singular integrals. Parabolic PDEs such as the heat equation can be viewed as vector-valued ODEs with respect to the time variable. The boundedness of vector-valued extensions of singular integrals is equivalent to the UMD condition of the vector space. One of my main research goals is to understand the UMD condition in limited range and multilinear contexts.

A recent research statement can be found here.