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2022年10月13日舉行線上專題學(xué)術(shù)報(bào)告.

報(bào)告題目：The L^p-boundedness of wave operators for fourth order Schr?dinger operator

時(shí) 間：2022年10月13日(星期四)14:30

騰訊會(huì)議ID: 115-692-757

報(bào)告摘要：

In this talk we will consider the L^p-bounds of wave operators W(H,) associated with bi-Schr?dinger operators H=+V(x) on R. Under a suitable decay condition on V and the absence of embedded eigenvalues of H, we first prove that the wave and dual wave operators are bounded on L^p(R) for all 1<p<. This result is further extended to the weighted L^p-boundedness with the sharp A_p-bounds for general even A_p-weights and to the boundedness on the Sobolev spaces W^{s,p}(R). For the limiting case p=1, we also obtain several weak-type boundedness, including W(H,)B(L^1, L^) and B(H^1, L^1). These results especially hold whatever the zero energy is a regular point or a resonance. Next, for the case that zero is a regular point, we prove that the wave operators are neither bounded on L^1(R) nor on L^(R), and they are even not bounded from L^(R) to BMO(R) if V is compactly supported. Finally, as applications, we can deduce the L^p-L^q decay estimates for the propagator e^{-itH} with pairs (1/p,1/q) belonging to certain region of R^2, as well as the H?rmander-type L^p-boundedness theorem for the spectral multiplier f(H). This is a joint-work with H. Mizutani and Zijun Wan.

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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)主持過多項(xiàng)國(guó)家自然科學(xué)基金面上項(xiàng)目, 也曾主持過教育部科學(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)教育部長(zhǎng)江學(xué)者及創(chuàng)新團(tuán)隊(duì)(偏微分方程)建設(shè).

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萃英學(xué)院

2022年10月10日