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Harmonic Analysis Graduate Student Seminar May 10, 2017 (10:30 AM PDT - 12:00 PM PDT)
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Location: MSRI: Baker Board Room
Speaker(s) Eunhee Jeong (Seoul National University), Jongchon Kim (University of Wisconsin-Madison)
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Jongchon Kim

Title: Bounds for the maximal Bochner-Riesz operators at the critical index.

Abstract. I will talk about a classical result of Stein-Taibleson-Weiss that the maximal Bochner-Riesz operator at the critical index is bounded from the real Hardy space H^p to weak L^p when 0<p<1. The original proof uses the decay of the Bochner-Riesz kernel in a crucial way. I will present a proof suggested by Andreas Seeger that avoids the use of the decay.



Eunhee Jeong.

Title : Uniform Sobolev inequalities in ${\mathbb R}^d$.

Abstract : In this talk, we observe uniform Sobolev inequalities for the second order differential operators $P(D)$ in ${\mathbb R}^d$, $d\ge 3$, focussing on their necessary conditions. As direct applications, we obtain the Carleman inequalities and the unique continuation for the differential inequality $P(D)u|\le |Vu|$. This is based on the joint work with Yehyun Kwon and Sanghyuk Lee.

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