Harmonic Analysis Seminar: The epsilon-removal principle

Seminar | March 20 | 1:10-2 p.m. | 736 Evans Hall

 Zirui Zhou, UC Berkeley

 Department of Mathematics

The $\varepsilon $–removal lemma of Tao converts a near-global family of bounds $\|Tf\|_{L^q(B(0,r)} \le O(r^\varepsilon \|f\|_{L^p})$ (as $r\to \infty $) to $\|Tf\|_{L^q(\mathbb R^d)} \le O( \|f\|_{L^{p+\delta }})$, for certain specific linear operators $T$. If the former holds for all positive $\varepsilon >0$ then one obtains a global bound with any exponent strictly $ >p$ on the right-hand side. This lemma is used to complete Guth's analysis of the Fourier “extension” operator. The proof and some applications of the result will be discussed.