You are cordially invited to the seminar organized by the Department of Mathematics.<\/p>\n
Speaker: Lingxiao Zhang (University of Wisconsin-Madison)<\/p>\n
“Real Analytic Singular Radon Transforms With Product Kernels: Necessity of the Stein-Street condition”<\/p>\n
Abstract: We discuss operators of the form<\/p>\n
Tf(x)=\u03c8(x)\u222bf(\u03b3_t (x))K(t)dt,<\/p>\n
where \u03c8(x)\u2208C_c^\u221e (R^n), \u03b3_t (x) is a real analytic function of (t,x) mapping from a neighborhood of (0,0)\u2208R^N\u00d7R^n into R^n satisfying \u03b3_0 (x)\u2261x, 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 \u03b3_t (x), in the special case when K(t) is a Calder\u00f3n-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 \u03b3_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.<\/p>\n
Date: Wednesday, 7 December 2022
\nTime: 16:00 GMT+3
\nPlace: Zoom<\/p>\n
To request the event link, please send a message to f.atay@bilkent.edu.tr<\/p>\n","protected":false},"excerpt":{"rendered":"
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)=\u03c8(x)\u222bf(\u03b3_t (x))K(t)dt, where \u03c8(x)\u2208C_c^\u221e (R^n), \u03b3_t (x) is a real analytic [\u2026] <\/p>\n