You are cordially invited to the seminar organized by the Department of Mathematics.
Speaker: Lingxiao Zhang (University of Wisconsin-Madison)
“Real Analytic Singular Radon Transforms With Product Kernels: Necessity of the Stein-Street condition”
Abstract: We discuss operators of the form
Tf(x)=ψ(x)∫f(γ_t (x))K(t)dt,
where ψ(x)∈C_c^∞ (R^n), γ_t (x) is a real analytic function of (t,x) mapping from a neighborhood of (0,0)∈R^N×R^n into R^n satisfying γ_0 (x)≡x, and K(t) is a product kernel with small support in R^N. The celebrated work of Christ, Nagel, Stein, and Wainger studied such operators with smooth γ_t (x), in the special case when K(t) is a Calderón-Zygmund kernel. Street and Stein generalized their work to (for instance) the product kernel case, and gave sufficient conditions for the L^p boundedness of such operators for all such kernels K. In this talk, we will state that when γ_t (x) is real analytic, the Stein-Street condition is also necessary, and will also use several simple examples and graphs to illustrate this necessary and sufficient condition and explain the main ideas of the proof methods.
Date: Wednesday, 7 December 2022
Time: 16:00 GMT+3
Place: Zoom
To request the event link, please send a message to f.atay@bilkent.edu.tr