Boundedness of Singular integral operators and applications to Bochner-Riesz summability, Riesz transforms, and Hardy spaces.

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We aim to develop harmonic analysis methods to study singular integral operators and function spaces associated to these operators. We propose to study the long standing problem of convergence of Bochner-Riesz means in Fourier analysis, and investigate differential operators with non-smooth coefficients acting on rough domains, or acting on general spaces like manifolds. Expected outcomes are new techniques in harmonic analysis to be developed, with applications being solutions to a number of open problems in the theories of harmonic analysis, partial differential equations and function spaces.