Harmonic analysis: function spaces and partial differential equations

Harmonic Analysis has been instrumental to several fields of mathematics including complex analysis and partial differential equations which have had many applications in engineering and technology. This project aims to solve a number of difficult fundamental problems in harmonic analysis which include to estimate singular integrals with rough kernels acting on various types of metric spaces, to study function spaces associated to these rough operators and certain associated regularity estimates that have arisen from complex analysis and partial differential equations. Expected outcomes are the solutions of a number of important problems, new approaches and techniques to be developed and training for the future mathematicians of Australia.