Research Projects

Spherical maximal functions and their multilinear analogues on the Euclidean space have been studied by a number of leading mathematicians with expertise in mathematical analysis. These operators are well known to have numerous profound applications in theoretical as well as applicable topics. The literature on spherical maximal functions has been growing extensively well beyond the Euclidean setting. However, their multilinear analogues have attracted attention quite recently (over the past 10-12 years) and have thus far been studied mainly in the context of the Euclidean spaces only. The Heisenberg group is a primary example of the broad class of nilpotent Lie groups, and harmonic analysis on these groups is a very active area of research with interests lying in mathematics and physics. Having the analytical or geometrical theory and applications that are established in Euclidean spaces, one looks to establish relevant analogues in the context of these groups. Owing to their applicability, it is therefore quite natural and interesting to systematically study the bilinear spherical maximal functions on the Heisenberg group.