Department of Mathematics

Indian Institute of Science

Bangalore 560 012

 

SEMINAR

 

Speaker

:

 Sanjay P. K.
Affiliation : IISc, Bangalore.

Subject Area

:

Mathematics

 

Venue

:

Department of Mathematics, Lecture Hall I

 

Time

:

11.30 a.m.- 12.30pm

 

Date  

:

October29, 2012 (Monday)

Title

:

"Riesz transforms associated with Heisenberg groups and Grushin operator"
Abstract

:

We characterize the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order Riesz transforms associated to the Hermite operator. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to special Hermite and Laguerre expansions. Next we study the Riesz transforms associated to the Grushin operator $ G = -\Delta-|x|^2 \partial_t^2 $ on $\R^{n+1}$. We prove that both the first order and higher order Riesz transforms are bounded on $ L^p(\R^{n+1}).$ We also prove that norms of the first order Riesz transforms are independent of the dimension $n$.