【廿周年院庆学术报告24】 · 【和山数学论坛第328期】

一、报告题目：Limited range extrapolation with quantitative bounds and applications

二、主讲人：司增艳教授

三、时间：2022年10月13日(周四) 上午10:00-11:30    

四、地点：腾讯会议, 会议ID：276-806-787

报告摘要：In recent years, sharp or quantitative weighted inequalities have attracted considerable attention on account of $A_2$ conjecture solved by Hyt\"{o}nen. Advances have greatly improved conceptual understanding of classical objects such as Calder\'{o}n-Zygmund operators. However, plenty of operators do not fit into the class of Calder\'{o}n-Zygmund operators and fail to be bounded on all $L^p(w)$ spaces for $p \in (1, \infty)$ and $w \in A_p$. In this paper we develop Rubio de Francia extrapolation with quantitative bounds to investigate quantitative weighted inequalities for operators beyond the (multilinear) Calder\'{o}n-Zygmund theory. We mainly establish a quantitative multilinear limited range extrapolation in terms of exponents $p_i \in (\p_i^-, \p_i^+)$ and weights $w_i^{p_i} \in A_{p_i/\p_i^-} \cap RH_{(\p_i^+/p_i)'}$, $i=1, \ldots, m$, which refines a result of Cruz-Uribe and Martell. We also present an extrapolation from multilinear operators to the corresponding commutators. Additionally, our result is quantitative and allows us to extend special quantitative estimates in the Banach space setting to the quasi-Banach space setting. Our proof is based on an off-diagonal extrapolation result with quantitative bounds. Finally, we present various applications to illustrate the utility of extrapolation by concentrating on quantitative weighted estimates for some typical multilinear operators such as bilinear Bochner-Riesz means, bilinear rough singular integrals, and multilinear Fourier multipliers. In the linear case, based on the Littlewood-Paley theory, we include weighted jump and variational inequalities for rough singular integrals.

报告人简介：司增艳，男，教授，硕士生导师，专业为调和分析及其应用。主持完成国家自然科学基金项目2 项、河南省自然科学基金面上项目1 项、河南省高等学校重点科研项目1项、河南省高校基本科研业务费项目1项。获河南省科学技术进步奖三等奖 1 项、河南省自然科学优秀学术论文二等奖 2 项。

主要从事多线性算子的有界性问题研究：在奇异积分理论和多线性算子理论等领域上发表论文 30 多篇，其中在《J. Reine Angew. Math.》、《J. Fourier Anal. Appl.》、《Nonlinear Anal.》、《Sci. China Math.》、《Forum Math. 》、《Potential Anal.》、《Bull. Sci. Math. 》等 SCI 期刊上有 20 篇。

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