赵发友

    赵发友,教授/数学系党总支书记

    邮箱:fyzhao@shu.edu.cn

    电话:021-66135302


    研究领域:调和分析及其应用


    教育经历:

    2007/9-2010/7, 北京师范大学, 数学学院, 博士

    2008/10-2009/10,University of Missouri-Columbia,数学系,博士生,国家留学基金委公派研究生项目


    工作经历:

    2020/3-至今,古天乐代言太阳集团,数学系,教授

    2014/3-2020/2,古天乐代言太阳集团,数学系,副教授

    2014/11-2015/11,University of Wisconsin-Milwaukee,数学系,访问学者,国家留学基金委青年骨干教师项目

    2012/7-2014/2,古天乐代言太阳集团,数学系,讲师

    2010/7-2012/6,古天乐代言太阳集团,数学系,博士后


    代表性科研项目:

    1. 国家自然科学基金面上项目, 11971295, 广义球面平均的若干问题, 2020-01至2023-12, 在研, 主持

    2. 国家自然科学基金青年基金项目, 11201287, 与Hardy算子相关的权函数的特征及其应用, 2013-01至2015-12, 已结题, 主持


    代表性学术论文:

    32. Liu, Rui; Zhao, Fayou* Boundedness of bilinear Dunkl-Hausdorff operators on products of Lebesgue and Morrey spaces. Integral Transforms Spec. Funct. 33 (2022), no. 9, 747–760.

    31. Zhou, Jing; Zhao, Fayou* Boundedness of the fractional Hardy-Littlewood maximal operator on weighted Morrey spaces. Anal. Math. Phys. 12 (2022), no. 4, Paper No. 87, 13 pp.

    30. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* Bochner-Riesz means and K-functional on Triebel-Lizorkin spaces. Numer. Funct. Anal. Optim. 43 (2022), no. 3, 273–306.

    29. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* Maximal estimates for an oscillatory operator. Nonlinear Anal. 218 (2022), Paper No. 112792, 24 pp.

    28. Chen, Jie Cheng; Fan, Da Shan; Zhao, Fa You* Approximation of the fractional Schrödinger propagator on compact manifolds. Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 10, 1485–1496.

    27. Zhao, Fayou*; Zhou, Hongxiu Variation inequality for the two-dimensional discrete Hardy-Littlewood maximal function. Results Math. 76 (2021), no. 4, Paper No. 170, 17 pp.

    26. Zhao, Fayou*; Liu, Rui Sharp inequalities between Lp-norms for the higher dimensional Hardy operator and its dual. Math. Inequal. Appl. 24 (2021), no. 1, 275–289.

    25. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou Bochner-Riesz means on block-Sobolev spaces in compact Lie group. J. Aust. Math. Soc. 109 (2020), no. 2, 176–192.

    24. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* On the rate of almost everywhere convergence of combinations and multivariate averages. Potential Anal. 51 (2019), no. 3, 397–423.

    23. Zhao, Fayou*; Ma, Liqin Higher-dimensional weighted Knopp type inequalities. Math. Inequal. Appl. 22 (2019), no. 2, 619–629.

    22. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* Littlewood-Paley functions and Sobolev spaces. Nonlinear Anal. 184 (2019), 273–297.

    21. Fan, Dashan; Zhao, Fayou* Sharp constants for multivariate Hausdorff q-inequalities. J. Aust. Math. Soc. 106 (2019), no. 2, 274–286.

    20. Fan, Dashan; Zhao, Fayou* Certain bilinear operators on Morrey spaces. Hokkaido Math. J. 47 (2018), no. 1, 143–159.

    19. Fan, Dashan; Zhao, Fayou* Approximation properties of combination of multivariate averages on Hardy spaces. J. Approx. Theory 223 (2017), 77–95.

    18. Guo, Jiuhua; Zhao, Fayou* Some q-inequalities for Hausdorff operators. Front. Math. China 12 (2017), no. 4, 879–889.

    17. Fan, Dashan; Zhao, Fayou* Block-Sobolev spaces and the rate of almost everywhere convergence of Bochner-Riesz means. Constr. Approx. 45 (2017), no. 3, 391–405.

    16. Fan, Dashan; Wu, Huoxiong; Zhao, Fayou* Transference of certain maximal Hilbert transforms on the torus. Pacific J. Math. 284 (2016), no. 2, 343–364.

    15. Gao, Guilian; Zhao, Fayou* Sharp weak bounds for Hausdorff operators. Anal. Math. 41 (2015), no. 3, 163–173.

    14. Guo, Jiu Hua; Sun, Li Jing; Zhao, Fa You* Hausdorff operators on the Heisenberg group. Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 11, 1703–1714.

    13. Fan, Dashan; Zhao, Fayou* Product Hardy operators on Hardy spaces. Tokyo J. Math. 38 (2015), no. 1, 193–209.

    12. Zhao, Fayou*; Lu, Shanzhen The best bound for n-dimensional fractional Hardy operators. Math. Inequal. Appl. 18 (2015), no. 1, 233–240.

    11. Fan, Da Shan; Zhao, Fa You* Multilinear fractional Hausdorff operators. Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 8, 1407–1421.

    10. Zhao, Fayou*; Fu, Zunwei; Lu, Shanzhen Mp weights for bilinear Hardy operators on Rn. Collect. Math. 65 (2014), no. 1, 87–102.

    9. Lu, Shanzhen; Yan, Dunyan; Zhao, Fayou* Sharp bounds for Hardy type operators on higher-dimensional product spaces. J. Inequal. Appl. 2013, 2013:148, 11 pp.

    8. Zhao, Fayou; Lu, Shanzhen A characterization of λ-central BMO space. Front. Math. China 8 (2013), no. 1, 229–238.

    7. Zhao, FaYou; Fu, ZunWei; Lu, ShanZhen Endpoint estimates for n-dimensional Hardy operators and their commutators. Sci. China Math. 55 (2012), no. 10, 1977–1990.

    6. Si, Zengyan; Zhao, Fayou* Necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted Morrey spaces. Abstr. Appl. Anal. 2012, Art. ID 929381, 14 pp.

    5. Zhao, Fayou A note on commutators of Hardy operators. Math. Nachr. 285 (2012), no. 10, 1294–1298.

    4. Fu, Zunwei; Grafakos, Loukas; Lu, Shanzhen; Zhao, Fayou* Sharp bounds for m-linear Hardy and Hilbert operators. Houston J. Math. 38 (2012), no. 1, 225–244.

    3. Grafakos, Loukas; Liu, Liguang; Lu, Shanzhen; Zhao, Fayou The multilinear Marcinkiewicz interpolation theorem revisited: the behavior of the constant. J. Funct. Anal. 262 (2012), no. 5, 2289–2313.

    2. Fu, ZunWei; Lu, ShanZhen; Zhao, FaYou Commutators of n-dimensional rough Hardy operators. Sci. China Math. 54 (2011), no. 1, 95–104.

    1. Lu, Shan Zhen; Zhao, Fa You CBMO estimates for multilinear Hardy operators. Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 7, 1245–1254.


    代表性论著:

    1. Shanzhen Lu, Zunwei Fu, Fayou Zhao, Shaoguang Shi, Hardy operators on Euclidean spaces and related topics, World Scientific Publishing Co. Pte. Ltd. 2023. 234 pp. ISBN: 978-981-125-367-6, https://doi.org/10.1142/12762.


    (最后更新日期:2022.10.20)

    赵发友

      赵发友,教授/数学系党总支书记

      邮箱:fyzhao@shu.edu.cn

      电话:021-66135302


      研究领域:调和分析及其应用


      教育经历:

      2007/9-2010/7, 北京师范大学, 数学学院, 博士

      2008/10-2009/10,University of Missouri-Columbia,数学系,博士生,国家留学基金委公派研究生项目


      工作经历:

      2020/3-至今,古天乐代言太阳集团,数学系,教授

      2014/3-2020/2,古天乐代言太阳集团,数学系,副教授

      2014/11-2015/11,University of Wisconsin-Milwaukee,数学系,访问学者,国家留学基金委青年骨干教师项目

      2012/7-2014/2,古天乐代言太阳集团,数学系,讲师

      2010/7-2012/6,古天乐代言太阳集团,数学系,博士后


      代表性科研项目:

      1. 国家自然科学基金面上项目, 11971295, 广义球面平均的若干问题, 2020-01至2023-12, 在研, 主持

      2. 国家自然科学基金青年基金项目, 11201287, 与Hardy算子相关的权函数的特征及其应用, 2013-01至2015-12, 已结题, 主持


      代表性学术论文:

      32. Liu, Rui; Zhao, Fayou* Boundedness of bilinear Dunkl-Hausdorff operators on products of Lebesgue and Morrey spaces. Integral Transforms Spec. Funct. 33 (2022), no. 9, 747–760.

      31. Zhou, Jing; Zhao, Fayou* Boundedness of the fractional Hardy-Littlewood maximal operator on weighted Morrey spaces. Anal. Math. Phys. 12 (2022), no. 4, Paper No. 87, 13 pp.

      30. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* Bochner-Riesz means and K-functional on Triebel-Lizorkin spaces. Numer. Funct. Anal. Optim. 43 (2022), no. 3, 273–306.

      29. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* Maximal estimates for an oscillatory operator. Nonlinear Anal. 218 (2022), Paper No. 112792, 24 pp.

      28. Chen, Jie Cheng; Fan, Da Shan; Zhao, Fa You* Approximation of the fractional Schrödinger propagator on compact manifolds. Acta Math. Sin. (Engl. Ser.) 37 (2021), no. 10, 1485–1496.

      27. Zhao, Fayou*; Zhou, Hongxiu Variation inequality for the two-dimensional discrete Hardy-Littlewood maximal function. Results Math. 76 (2021), no. 4, Paper No. 170, 17 pp.

      26. Zhao, Fayou*; Liu, Rui Sharp inequalities between Lp-norms for the higher dimensional Hardy operator and its dual. Math. Inequal. Appl. 24 (2021), no. 1, 275–289.

      25. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou Bochner-Riesz means on block-Sobolev spaces in compact Lie group. J. Aust. Math. Soc. 109 (2020), no. 2, 176–192.

      24. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* On the rate of almost everywhere convergence of combinations and multivariate averages. Potential Anal. 51 (2019), no. 3, 397–423.

      23. Zhao, Fayou*; Ma, Liqin Higher-dimensional weighted Knopp type inequalities. Math. Inequal. Appl. 22 (2019), no. 2, 619–629.

      22. Chen, Jiecheng; Fan, Dashan; Zhao, Fayou* Littlewood-Paley functions and Sobolev spaces. Nonlinear Anal. 184 (2019), 273–297.

      21. Fan, Dashan; Zhao, Fayou* Sharp constants for multivariate Hausdorff q-inequalities. J. Aust. Math. Soc. 106 (2019), no. 2, 274–286.

      20. Fan, Dashan; Zhao, Fayou* Certain bilinear operators on Morrey spaces. Hokkaido Math. J. 47 (2018), no. 1, 143–159.

      19. Fan, Dashan; Zhao, Fayou* Approximation properties of combination of multivariate averages on Hardy spaces. J. Approx. Theory 223 (2017), 77–95.

      18. Guo, Jiuhua; Zhao, Fayou* Some q-inequalities for Hausdorff operators. Front. Math. China 12 (2017), no. 4, 879–889.

      17. Fan, Dashan; Zhao, Fayou* Block-Sobolev spaces and the rate of almost everywhere convergence of Bochner-Riesz means. Constr. Approx. 45 (2017), no. 3, 391–405.

      16. Fan, Dashan; Wu, Huoxiong; Zhao, Fayou* Transference of certain maximal Hilbert transforms on the torus. Pacific J. Math. 284 (2016), no. 2, 343–364.

      15. Gao, Guilian; Zhao, Fayou* Sharp weak bounds for Hausdorff operators. Anal. Math. 41 (2015), no. 3, 163–173.

      14. Guo, Jiu Hua; Sun, Li Jing; Zhao, Fa You* Hausdorff operators on the Heisenberg group. Acta Math. Sin. (Engl. Ser.) 31 (2015), no. 11, 1703–1714.

      13. Fan, Dashan; Zhao, Fayou* Product Hardy operators on Hardy spaces. Tokyo J. Math. 38 (2015), no. 1, 193–209.

      12. Zhao, Fayou*; Lu, Shanzhen The best bound for n-dimensional fractional Hardy operators. Math. Inequal. Appl. 18 (2015), no. 1, 233–240.

      11. Fan, Da Shan; Zhao, Fa You* Multilinear fractional Hausdorff operators. Acta Math. Sin. (Engl. Ser.) 30 (2014), no. 8, 1407–1421.

      10. Zhao, Fayou*; Fu, Zunwei; Lu, Shanzhen Mp weights for bilinear Hardy operators on Rn. Collect. Math. 65 (2014), no. 1, 87–102.

      9. Lu, Shanzhen; Yan, Dunyan; Zhao, Fayou* Sharp bounds for Hardy type operators on higher-dimensional product spaces. J. Inequal. Appl. 2013, 2013:148, 11 pp.

      8. Zhao, Fayou; Lu, Shanzhen A characterization of λ-central BMO space. Front. Math. China 8 (2013), no. 1, 229–238.

      7. Zhao, FaYou; Fu, ZunWei; Lu, ShanZhen Endpoint estimates for n-dimensional Hardy operators and their commutators. Sci. China Math. 55 (2012), no. 10, 1977–1990.

      6. Si, Zengyan; Zhao, Fayou* Necessary and sufficient conditions for boundedness of commutators of the general fractional integral operators on weighted Morrey spaces. Abstr. Appl. Anal. 2012, Art. ID 929381, 14 pp.

      5. Zhao, Fayou A note on commutators of Hardy operators. Math. Nachr. 285 (2012), no. 10, 1294–1298.

      4. Fu, Zunwei; Grafakos, Loukas; Lu, Shanzhen; Zhao, Fayou* Sharp bounds for m-linear Hardy and Hilbert operators. Houston J. Math. 38 (2012), no. 1, 225–244.

      3. Grafakos, Loukas; Liu, Liguang; Lu, Shanzhen; Zhao, Fayou The multilinear Marcinkiewicz interpolation theorem revisited: the behavior of the constant. J. Funct. Anal. 262 (2012), no. 5, 2289–2313.

      2. Fu, ZunWei; Lu, ShanZhen; Zhao, FaYou Commutators of n-dimensional rough Hardy operators. Sci. China Math. 54 (2011), no. 1, 95–104.

      1. Lu, Shan Zhen; Zhao, Fa You CBMO estimates for multilinear Hardy operators. Acta Math. Sin. (Engl. Ser.) 26 (2010), no. 7, 1245–1254.


      代表性论著:

      1. Shanzhen Lu, Zunwei Fu, Fayou Zhao, Shaoguang Shi, Hardy operators on Euclidean spaces and related topics, World Scientific Publishing Co. Pte. Ltd. 2023. 234 pp. ISBN: 978-981-125-367-6, https://doi.org/10.1142/12762.


      (最后更新日期:2022.10.20)