The aim of this project is to study Fourier multipliers and related convolution type operators with discontinuous symbols on Banach function spaces beyond classical Lebesgue spaces. Our team is mainly interested in Fredholm criteria, that is, necessary and sufficient conditions for the invertiblility of a given operator in a certain algebra of operators modulo the ideal of compact operators. The project consists of four related tasks. Two tasks will involve two colleagues from Mexico and the United Kingdom, two other tasks will involve two MSc students.
Team members: Oleksiy Karlovych and Cláudio Fernandes.