The principal purpose of the project is to obtain new information on two-weight inequality for Bergman projection. The case of the classical Bergman projection is of particular interest and has been proven to be difficult to handle in the existing literature. Bergman projection is closely related to Hankel- and Toeplitz-type operators. One goal is to obtain conclusive results on Hankel operators induced by doubling weights. We aim for a scalar-valued counter example to the sixth problem of Halmos - polynomially bounded operator problem - by considering small Bergman spaces.

2023

2027