Speaker: Mithun Bhowmik, IISc Bangalore

Time & Date: 4 pm, Monday, 01 August 2022

Venue: Ramanujan Hall

Title: Hardy and Adams Type Inequalities for the Fractional Laplace-Beltrami Operator on Noncompact Symmetric Spaces  

Abstract. In this talk, we will discuss Hardy and Adams type inequalities for fractional powers of the Laplace-Beltrami operator on Riemannian symmetric space $X$ of noncompact type. We use solutions to the extension problem in combination with the ground state representation method (of Frank et al) to establish Hardy’s inequality. We will discuss $L^p - L^q$ mapping properties of the extension operator and get an improvement over the corresponding results on Euclidean spaces. This is a joint work with Sanjoy Pusti. Next, we will discuss sharp Adams type inequalities on Sobolev spaces $W^{\alpha,n/\alpha}(X)$ of any fractional order $\alpha < n$ on $X$ with dimension $n$.