Description
Analysis Seminar.
Speaker: Prof. S. Thangavelu
Affiliation: IISc, Bengaluru.
Date and Time: Tuesday 05 March, 11:35 am - 12:30 pm.
Venue: Room 216, Department of Mathematics.
Title: Lacunary Spherical maximal function on the Heisenberg group.
Abstract: We investigate the $L^p$ boundedness of the lacunary maximal
function $A_rf$ associated to the spherical means on the Heisenberg group.
By suitable adaptation of an approach of M. Lacey in the Euclidean case,
we obtain sparse bounds for these maximal functions, which lead to new
unweighted and weighted estimates. In order to prove the result, several
properties of the spherical means have to be accomplished, namely, the
$L^p$ improving property of the operator $A_rf$ and a continuity property
of the difference $A_rf-\tau_y A_rf$, where $\tau_yf(x)=f(xy^{-1})$ is the
right translation operator. This is a joint work with Hait, Bagchi and
Roncal.