Tue, March 5, 2019
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11:00am [11:35am] Prof. S. Thangavelu, IISc, Bengaluru
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.

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