Research areas of the group include:
- convolution operators, singular integrals, maximal operators, Fourier multipliers;
- Lp-improving phenomenon, Lp- boundedness of generalized and singular Radon transforms;
- Fourier analysis on the Heisenberg group and on nilpotent Lie groups;
- invariant differential operators on Lie groups: local solvability and Lp- boundedness of spectral multipliers;
- methods of commutative and non-commutative Fourier analysis in complex analysis: spaces of holomorphic function on symmetric Siegel domains, boundary values and estimates for Bergman projectors.