薛慶營檢視原始碼討論檢視歷史
|
薛慶營，男，北京師範大學文理學院教授,理學博士、博士生導師。
人物簡歷
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.
研究領域
調和分析及其應用。1998年畢業於曲阜師範大學，獲學士學位，2001年畢業於北京師範大學，獲碩士學位，2004年畢業於北京師範大學，獲博士學位。曾先後在德國和日本做博士後研究工作，並在2009-2010在美國加州大學伯克利分校做訪問學者一年，2017年在美國堪薩斯大學做高級訪問學者半年。已經培養畢業7名博士,11名碩士。2019年獲評北京師範大學優秀博士論文指導教師。2021年獲評第十七屆北京師範大學教學名師；2021年獲評北京高校優秀教學管理人員。
研究成果
在線性算子和多線性算子研究以及算子的雙權刻畫等方面獲得了一系列重要成果。已在美國、法國等國際著名或重要數學雜誌如 J. Math. Pure. Appl.；Revista Matemática Iberoamericana.；J. Funct. Anal. ； J. Fourier Anal. Appl. 等接受和發表文章 100餘篇， 3篇發表在由J. Liouville創建的國際著名的法國數學刊物 J. Math. Pure. Appl. （純數學與應用數學雜誌）上。
研究興趣
My general areas of interests are in
Harmonic analysis; Harmonic analysis on groups
Harmonic analysis techniques to PDE;
Functions spaces.
科研項目
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.
學術成果
論著
● 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).[1]