个人简介

薛庆营，男，教授、理学博士、博士生导师。入选《教育部新世纪优秀人才支持计划》。研究领域：调和分析及其应用。1998年毕业于曲阜师范大学，获学士学位，2001年毕业于北京师范大学，获硕士学位，2004年毕业于北京师范大学，获博士学位。曾先后在德国和日本做博士后研究工作，并在2009-2010在美国加州大学伯克利分校做访问学者一年，2017年在美国堪萨斯大学做高级访问学者半年。已经培养毕业7名博士,11名硕士。2019年获评北京师范大学优秀博士论文指导教师。2021年获评第十七届北京师范大学教学名师；2021年获评北京高校优秀教学管理人员。

研究成果简介： 薛庆营教授在线性算子和多线性算子研究以及算子的双权刻画等方面获得了一系列重要成果。已在美国、法国等国际著名或重要数学杂志如 J. Math. Pure. Appl.；Revista Matemática Iberoamericana.；J. Funct. Anal. ； J. Fourier Anal. Appl. 等接受和发表文章 100余篇， 3篇发表在由J. Liouville创建的国际著名的法国数学刊物 J. Math. Pure. Appl. （纯数学与应用数学杂志）上。

研究背景简介： 从多线性算子的发展来看，首先用多线性观点来研究一类奇异积分算子的是Coifman和Meyer ，两人在七十年代和八十年代的一系列出色的研究，开创了多线性算子研究的先河。随之，很多著名调和分析专家在此领域做出了很好的工作。如Christ 和Journe，Kenig和Stein，Grafakos和Torres等的工作。最为著名的工作还有Christ, Tao 及其合作者的一系列的出色研究成果，近期还有Lerner, Perez等人的大量工作等。可以说，多线性算子的研究一直是调和分析发展的主流方向之一。

主要经历

● 1998—2001 Graduate studies of Mathematics at Beijing Normal University, P. R. China. Advisors were Prof. Yong Ding and Prof. Shanzhen Lu.

● 2001-2004 PhD Student in Department of Mathematics, Beijing Normal University, P. R. China. Advisors were Prof. Yong Ding and Prof. Shanzhen Lu.

● 2004.-2005 Postdoc in Friedrich-Schiller-University Jena, Mathematical Institute, Germany.

● 2005- 2006 Postdoc position in Kwansei Gakuin University, Japan.

● Since 2006.6 Working at School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, P. R. China.

● 2009.11- 2010.12 Visiting Scholar at Department of Mathematics, University of California, Berkeley, Berkeley, CA 94720-3840 USA.

● 2017.7- 2018.1 Senior Visiting Scholar at Department of Mathematics, The University of Kansas, Lawrence , KS 66045-7594 USA.

研究兴趣

My general areas of interests are in

● Harmonic analysis; Harmonic analysis on groups

● Harmonic analysis techniques to PDE;

● Functions spaces.

教学工作

2018.9-2019.2 数学分析 I

2019.3-2019.7 数学分析 II

2019.9-2020.1 数学分析III

2020.3-2020.7 实变函数

科研项目

●National Sciences Foundation of China for Young Scholar No. 10701010, 2008-2010, Singular integrals with variable kernels along surfaces and parabolic type.

●Scientific Research Foundation for the Returned Overseas Chinese Scholars in 2007, State Education Ministry.

●Supported by Program for New Century Excellent Talents in University, No. NCET-13-0065, 2014-2016.

●National Sciences Foundation of China, No. 11471041, 2015-2018. On the boundedness of multilinear operators and applications..

●National Sciences Foundation of China, No. 11871101, 2019-2022. on the study of some important topics related to multilinear operators.

代表性论著

● On weighted Compactness of commutators of bilinear maximal Calderon-Zygmund singular integral operators, (with Shifen Wang), Forum Math. To appear.

● On Some properties of dyadic operators, (with H. Gu and K. Yabuta), Taiwanese J. Math. To appear.

● The Limiting Weak Type Behaviors of the Strong Maximal Operators, (with M. Qin and H. Wu), Banach J. Math. Anal. To appear.

● Regularity of local bilinear maximal operator, (with F. Liu and S. Wang), Results in Mathematics. To appear.

● On weighted Compactness of Commutator of semi-group maximal function and fractional integrals associated to Schr\"odinger operators (with S. Wang), Rev. Mat. Complut. To appear.

● On the regularity and continuity of the multilinear fractional strong maximal operators (with F. Liu, K. Yabuta), Math. Nachr.To appear.

● Weighted estimates for maximal bilinear rough singular integrals via sparse dominations, (with Z. Wang, and X. Duan),Collect. Math. To appear.

● Regularity and continuity of commutators of multilinear maximal operators (with F. Liu, P. Zhang), New York J Math.To appear.

● Sobolev boundedness and continuity for commutators of the local Hardy–Littlewood maximal function, (with F. Liu and K. Yabuta), Ann. Acad. Sci. Fenn. Math. To appear.

● On oscillatory singular integrals and their commutators with non-convolutional H\"{o}lder class kernels, (with F. Liu and S. Wang), Banach J. Math. Anal. 15 (2021), no. 3, Paper No. 51, 35 pp.

● Weighted Fr\'{e}chet-Kolmogorov theorem and compactness of vector-valued multilinear operators, (with K. Yabuta and J. Yan), J. Geom. Anal. 31 (2021), no. 10, 9891–9914.

● Multilinear Littlewood-Paley-Stein operators on non-homogeneous spaces, (with M. Cao), J. Geom. Anal. 31 (2021), no. 9, 9295–9337.

● XMO and weighted compact bilinear commutators, (with J. Tao, D. Yang and W. Yuan), J. Fourier Anal. Appl.27 (2021), no. 3, Paper No. 60, 34 pp.

● Weighted and unweighted Solyanik estimates for the multilinear strong maximal function, (with M. Qin), Results in Mathematics. 76 (2021), no. 1, Paper No. 6, 19 pp.

● Two weight characterizations for the multilinear local maximal operators, (with Y. Pan), Acta. Math. Sci. 41 (2021), no. 2, 596–608.

● Weighted estimates for bilinear Fourier multiplier operators with multiple weights, (with G.Hu,Z. Wang, K. Yabuta), J. Geom. Anal. 31 (2021), no. 2, 2152–2171.

● On the composition of rough singular integral operators, (with G.Hu, X.Lai), J. Geom. Anal. 31 (2021), no. 3, 2742–2765.

● Regularity and continuity of local multilinear maximal type operators, (with J. Hart and F. Liu). J. Geom. Anal.31 (2021), no. 4, 3405–3454.

● On the variation of the Hardy-Littlewood maximal functions on finite graphs, (with F. Liu),Collect. Math. 72 (2021), no. 2, 333–349.

● Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces, (with F. Liu, K. Yabuta). Sci. China Math. (2020), no. 5, 907-936.

● On the bilinear square Fourier multiplier operators associated with $g_{\lambda}^*$ function, (with Z. Li). Nagoya Math J. 239 (2020), 123-152.

● Regularity and continuity of the multilinear strong maximal operators, (with Feng Liu and K. Yabuta). J. Math. Pure. Appl.(9) 138 (2020), 204–241.

● Weak and strong type estimates for the multilinear pseudo-differential operators, (with M. Cao and K. Yabuta), J. Funct. Anal.278 (2020), no. 10, 108454, 46 pp.

● On compactness of commutators of multiplication and bilinear pseudodifferential operators and a new subspace of BMO, (with R.H. Torres). Revista Matemática Iberoamericana. 36 (2020), no. 3, 939–956.

● On rough singular integrals along real -analytic submanifolds, (with F. Liu and H. Wu). Forum Math. 32 (2020), no. 2, 361–380.

● On the boundedness of multilinear fractional strong maximal operator with multiple weights, (with M. Cao and K. Yabuta)，Pacific J. Math. . 303 (2019), No. 2, 491-518.

● A revisit on commutators of linear and bilinear fractional integral operator, (M.Cao). Tohoku Math J. 2019,303-318.

● Parametrized multilinear Littlewood-Paley operators on Hardy spaces, (with S. He). Taiwanese J. Math. 23 (2019), no. 1, 87-101.

● Compact bilinear commutators: the quasi-Banach space case, (with R.H. Torres, J. Yan). J. Anal. . 26 (2018), no. 2, 227-234.

● A note on Carleson embedding theorems, (with M. Cao, H. Tanaka, K. Yabuta). Publ. Math. Debrecen 93 (2018), no. 3-4, 517-523.

● On general multilinear square function with non-smooth kernels, (with H. Mahdi; Z.Si). Bull. Sci. Math. Bull. Sci. Math. 149 (2018), 1-22.

● Boundedness of bi-parameter Littlewood-Paley operators on product Hardy space, (with Z. Li). Rev. Mat. Complut. 31 (2018), no. 3, 713-745.

● Characterizations of the multiple Littlewood-Paley operators on product domains, (with F.Liu). Publ. Math. Debrecen 92 (2018), no. 3-4, 419-439.

● A characterization of two-weight norm inequality for Littlewood-Paley $g_{\lambda}^*$-function, (with M. Cao and K. Li). J. Geom. Anal. 28 (2018), no. 2, 842-865.

● Rough maximal singular integral and maximal operators supported by subvarieties on Triebel-Lizorkin spaces, (with F.Liu and K. Yabuta). Nonlinear Analysis: TMA. 171 (2018), 41-72.

● A non-homogeneous local Tb theorem for Littlewood-Paley $g^*_\lambda$-function with $L^p$-testing condition, (with M. Cao). Forum Math. 30 (2018), no. 2, 457-478.

● Corrigendum to ``On multilinear fractional strong maximal operator associated with rectangles and multiple weights'' [Rev. Mat. Iberoam. 33 (2017), no. 2, 555–572], (with M. Cao and K. Yabuta). Revista Matemática Iberoamericana. 34 (2018), no. 1, 475-479

● On the bilinear square Fourier multiplier operators and related multilinear square functions, (with Z. Si and K. Yabuta).Sci. China Math. 60 (2017), no. 8, 1477-1502

● On multilinear fractional strong maximal operator associated with rectangles and multiple weights, (with M. Cao and K. Yabuta). Revista Matemática Iberoamericana.33 (2017), NO. 2, 555-572

● Bi-parameter Littlewood-Paley operators with upper doubling measures, (with M. Cao). Illinois J. Math. 61 (2017), no. 1-2, 53-79.

● Compactness of maximal commutators of bilinear Calderón-Zygmund singular integral operators, (with Y. Ding and T. Mei). Some topics in harmonic analysis and applications, 163–175, Adv. Lect. Math. (ALM), 34, Int. Press, Somerville, MA, 2016.

● Certain Multi(sub)linear square functions, (with L. Grafakos and S. He). Potential Analysis. 45 (2016) , 55-64

● Characterization of two-weighted inequalities for multilinear fractional maximal operator, (with M. Cao). Nonlinear Analysis: TMA. 130 (2016) 214-228.

● Generalized commutators of multilinear Calderon-Zygmund operators, (with J. Yan). J. Math. Soc. Japan, 68 (2016), No.3, 1161-1168.

● Fractional type Marcinkiewicz integral operators on function spaces, (with K. Yabuta and J. Yan). Forum Mathematicum., 27 (2015), 3079-3109.

● Existence and boundedness of multilinear Littlewood-Paley operators on Campanato spaces, (with S. He, T. Mei and K. Yabuta). J. Math. Anal. Appl., 432 (2015) 86-102.

● Weighted version of Carleson measure and multilinear Fourier multiplier, (with W. Li and K. Yabuta). Forum Mathematicum, 27 No 2 (2015), 787-805.

● On the Theory of Multilinear Littlewood-Paley $g$-function, (with X. Peng and K. Yabuta). J. Math. Soc. Japan, 67 No.2, (2015) 535-559 .

● On multilinear Littlewood-Paley operators, (with X. Chen and K. Yabuta). Nonlinear Analysis: TMA, 115,(2015) 25-40.

● On multilinear square function and its applications to multilinear Littlewood-Paley operators with non-convolution type kernels, (with J. Yan). J. Math. Anal. Appl. 422, (2015), 1342-1362.

● A note on multilinear Muckenhoupt classes for multiple weights, (with S. Chen and H. Wu.). Studia Math, 223 (2014), 1-18.

● On the Boundedness of multilinear Littlewood-Paley g_{\lambda}^{*} function (with S. Shi and K. Yabuta). J. Math. Pure. Appl.101 (2014) 394-413.

● Weighted Estimates for Commutators of Vector-Valued Maximal Multilinear Operators, (with Z. Si). Nonlinear Analysis: TMA, 96 (2014) 96-108.

● Weighted Estimates for the iterated Commutators of Multilinear Maximal and Fractional Type Operators. Studia Math, 217 (2013), 97-122.

● Continuity property for the Commutators of Multilinear Calder\'on-Zygmund operators. (with W. Li). Forum Mathematicum, 25 (2013) 771-785.

● Smoothness of Extremizers of a Convolution Inequality. (with M. Christ) .
J. Math. Pure. Appl.(2) 97 (2012), no 2,120-141.

● A Remark to the L^2 boundedness of parametric Marcinkiewicz integral. (with Y. Ding, K. Yabuta). J. Math. Anal. Appl. 387(2), (2012) 691-697.

● Multilinear version of reversed H\"{o}lder inequality and its applications to multilinear Calder\'{o}n-Zygmund operators (with J. Yan). J. Math. Soc. Japan. 14, No.4 (2012), 1-17.

● Maximal operator for multilinear Calderon-Zygmund singular integral operators on weighted Hardy spaces. (with Li,Yabuta). J.Math.Anal.Appl. 373, 2, (2011) 384–392.

● Weighted Estimates for a Class of Multilinear Fractional Type Operators. (with Xi Chen). J. Math. Anal. Appl, 362, no. 2, (2010) pp. 355–373.

● Multilinear Calderon-Zygmund operators on weighted Hardy spaces. (with W. Li and K. Yabuta). Studia Math, 199, No. 1 (2010), 1-16

● On singular integral operators with rough kernel along surface. (with Y. Ding, K. Yabuta). Integr. Equ. Oper. Theory 42 (2010) 68,151–161.

● Boundedness of the Marcinkiewicz integrals with rough kernel associated to surfaces. (with Y. Ding, K. Yabuta). Tohoku Math. J. 62(2010) 233–262,

● On the boundedness of singular integrals with variable kernels (with K. Yabuta). Tohoku Math. J. vol. 61, no. 1, pp. 41–65, 2009

● Weighted estimates for the Multilinear commutators of the Littlewod-Paley operators (with Y. Ding). Science in China. Series A. 52(2009), No. 9. 1849--1868.

● Parabolic Littlewod-Paley operators (with Yong Ding and K. Yabuta). Math. Nachr. vol. 282, no. 1, pp. 125–141, 2009

● Parameterized Littlewood-Paley operators on Hardy and weak Hardy spaces (with Yong Ding and Shanzhen Lu). Math. Nachr. 280(2007), No. 4. 351--363.

● Weighted boundedness for parameterized Littlewood-Paley operators. (with Yong Ding). Taiwanese J. Math. 11(2007), No 4 1143--1165.

● Existence and boundedness of Parameterized Marcinkiewicz integral with rough kernel on Campanato spaces (with Yong Ding and K. Yabuta) Nagoya Math. J. 181 (2006), 103–148.

● Weak type (1, 1) bounds for a class of the Littlewood-Paley operators, J. Math. Soc. Japan, 57 (2005), no. 1, 184-194 ( with Yong Ding).

● Marcinkiewicz Integral on Hardy spaces, Integr. Equ. Oper. Theory 42 (2002), no. 2, 174-182 (with Yong Ding and Shanzhen Lu).

● On Marcinkiewicz Integral with homogeneous Kernels, J. Math. Anal. Appl. 245 (2000), no. 2, 471--488 (with Yong Ding and Shanzhen Lu).

学生培养

已经毕业博士生：

王志丹（Zhidan Wang）-------(南京工业大学)

章娟（Juan Zhang）-------(北京林业大学)

曹明明（Mingming Cao）-------(西班牙马德里数学中心博士后)

李正阳（Zhengyang Li）-------(湖南科技大学)

贺莎（Sha He）-------------(北京第二外国语学院)

严井泉（Jingquan Yan）-------(安庆师范大学)

已经毕业硕士生：

王志丹（Zhidan Wang) ------(北师大博士毕业)

张春梅 (Chunmei Zhang) -------

段昕辰 (Xinchen Duan）-------(美国雪城大学)

谷恒（Heng Gu）------- (北京金橙子科技股份有限公司)

曹明明（Mingming Cao）-------

严井泉（Jingquan Yan）-------

陈曦（Xi Chen）------------(剑桥大学博士后)

李文娟（Wenjuan Li）-------- (西北工业大学)

徐得三（Desan Xu）-----------

彭修香（Xiuxiang Peng）------(大庆中学)