#### PhD Thesis colloquium

##### Venue: LH-1, Mathematics Department

In 1976, E.M. Stein proved $L^p$ bounds for spherical maximal function on Euclidean space. The lacunary case was dealt on later by C.P. Calderon in 1979. In a recent paper, M. Lacey has proved sparse bound for these functions and $L^p$ bounds will follow immediately as a result.

In this talk, we will look at various maximal functions corresponding to spherical averages and find sparse bounds for those functions. We will also observe some weighted and unweighted estimates that will follow as a consequences.

First, we will show sparse bound for lacunary spherical maximal function on Heisenberg group . Next we move on to full spherical maximal function. Then we study lacunary maximal function corresponding to the spherical average on product of Heisenberg groups. Finally, we will revisit generalized spherical averages on Euclidean space and prove sparse bounds for the related maximal functions.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 14 Feb 2020