應(yīng)yl7703永利官網(wǎng)耿俊教授和楊四輩教授邀請(qǐng),華中師范大學(xué)堯小華教授將于2021年11月24日舉行線上專題學(xué)術(shù)報(bào)告.

報(bào)告題目：Kato smoothing and Strichartz estimates for fractional operators with Hardy potentials

時(shí) 間：2021年11月24日(星期三)14:30;

騰訊會(huì)議ID: 445 850 497.

報(bào)告摘要：

Let $0<\sigma<n/2$ and $H=(-\Delta)^\sigma+a|x|^{-2\sigma}$ be Schrodinger type operators on $\R^n$ with a sharp coupling constant $a\le -C_{\sigma,n}$ ( $C_{\sigma,n}$ is the best constant of Hardy's inequality of order $\sigma$). In the present talk, we will address that sharp global estimates for the resolvent and the solution to the time-dependent Schrodinger equation associated with $H$. In the case of the subcritical coupling constant $a>-C_{\sigma,n}$, we first prove the uniform resolvent estimates of Kato--Yajima type for all $0<\sigma<n/2$, which turn out to be equivalent to Kato smoothing estimates for the Cauchy problem. We then establish Strichartz estimates for $\sigma>1/2$ and uniform Sobolev estimates of Kenig--Ruiz--Sogge type for $\sigma\ge n/(n+1)$. In the critical coupling constant case $a=-C_{\sigma,n}$ , we show that the same results as in the subcritical case still hold for functions orthogonal to radial functions. This is a joint-work (To appear in CMP) with Haruya Mizutani.

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堯小華教授簡(jiǎn)介

堯小華,華中師范大學(xué)yl7703永利官網(wǎng)教授、博士生導(dǎo)師，2010年入選教育部新世紀(jì)人才計(jì)劃；主要從事調(diào)和分析與微分算子的研究；在色散方程、微分算子及函數(shù)空間等方向上開(kāi)展研究工作；主要學(xué)術(shù)成果發(fā)表在“Comm. Math. Phys.”、“Trans. AMS”、“Inter. Math. Res. Notices”、“J. Functional Analysis”、“Comm. Partial Differential equation”、Siam J. Math. Anal.等國(guó)際重要數(shù)學(xué)期刊上；連續(xù)主持過(guò)多項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目，也曾主持過(guò)教育部科學(xué)技術(shù)研究重點(diǎn)項(xiàng)目及新世紀(jì)優(yōu)秀人才計(jì)劃等多個(gè)科研項(xiàng)目；作為核心成員參與了華中師范大學(xué)創(chuàng)新團(tuán)隊(duì)（偏微分方程）建設(shè)。

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2021年11月21日