摘要本文主要讨论单位圆盘上指数权Bergman空间Aφp和Aφ∞(0 < p < ∞)之间由正Borel测度μ所诱导的Toeplitz算子Tμ,借助Berezin变换和平均函数刻画该类算子的有界性和紧性. | | 服务 | | | 加入引用管理器 | | E-mail Alert | | RSS | 收稿日期: 2020-07-07 | | 基金资助:国家自然科学基金(11971125,11971123);广东省高校重点科研平台与科研项目(2018KZDXM048)
| 通讯作者:王晓峰,E-mail:wxf@gzhu.edu.cnE-mail: wxf@gzhu.edu.cn | 作者简介: 何忠华,E-mail:zhonghuahe2010@163.com;刘柚岐,E-mail:youqi_liu@foxmail.com |
[1] Arroussi H., Pau J., Reproducing kernel estimates, bounded projections and duality on large weighted Bergman spaces, J. Geom. Anal., 2015, 25:2284-2312. [2] Arroussi H., Park I., Pau J., Schatten class Toeplitz operators acting on large weighted Bergman spaces, Studia Math., 2015, 229:203-221. [3] Asserda A., Hichame A., Pointwise estimate for the Bergman kernel of the weighted Bergman spaces with exponential weights, C. R. Math. Acad. Sci. Paris, 2014, 352(1):13-16. [4] Borichev A., Dhuez R., Kellay K., Sampling and interpolation in large Bergman and Fock spaces, J. Funct. Anal., 2007, 242:563-606. [5] Carleson L., An interpolation problem for bounded analytic functions, Amer. J. Math., 1958, 80:921-930. [6] Carleson L., Interpolation by bounded analytic functions and the corona problem, Ann. of Math., 1962, 76:547-559. [7] Constantin O., Pelaez J. A., Boundedness of the Bergman projection on Lp spaces with exponential weights, Bull. Sci. Math., 2015, 139:245-268. [8] Constantin O., Pelaez J. A., Integral operators, embedding theorems and a Littlewood-Paley formula on weighted Fock spaces, J. Geom. Anal., 2016, 26:1109-1154. [9] Duren P. L., Theory of Hp Spaces, Academic Press, New York, 1970. [10] Galanopoulos P., Pau J., Hankel operators on large weighted Bergman spaces, Ann. Acad. Sci. Fenn. Math., 2012, 37:635-648. [11] Girela D., Peláez J. A., Carleson measures, multipliers and integration operators for spaces of Dirichlet type, J. Funct. Anal., 2006, 241:334-358. [12] Hu Z. J., Lv, X. F., Toeplitz operators on Fock spaces Fp(φ), Integr. Equ. Oper. Theory, 2014, 80:33-59. [13] Hu Z. J., Lv X. F., Positive Toeplitz operators between different doubling Fock spaces, Taiwan. J. Math., 2017, 21(2):467-487. [14] Hu Z. J., Lv X. F., Schuster A. P., Bergman spaces with exponential weights, J. Funct. Anal., 2019, 276(5):1402-1429. [15] Lin P., Rochberg R., Hankel operators on the weighted Bergman spaces with exponential weights, Integr. Equ. Oper. Theory, 1995, 21:460-483. [16] Lin P., Rochberg R., Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights, Pacific J. Math., 1996, 173:127-146. [17] Lv X. F., Carleson measures and Toeplitz operators on doubling Fock spaces, Chin. Ann. Math. Ser. B, 2019, 40(3):349-362. [18] Oleinik V. L., Embedding theorems for weighted classes of harmonic and analytic functions, J. Sov. Math., 1978, 9:228-243. [19] Pau J., Peláez J. Á., Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights, J. Funct. Anal., 2010, 259:2727-2756. [20] Pau J., Peláez J. Á., Volterra type operators on Bergman spaces with exponential weights, Contemp. Math., 2012, 561:239-252. [21] Wang X. F., Cao G. F., Xia J., Toeplitz operators on Fock-Sobolev spaces with positive measure symbols, Science China Mathematics, 2014, 57:1443-1462. [22] Wang X. F., Cao G. F., Zhu K. H., BMO and Hankel operators on Fock-type spaces, J. Geom. Anal., 2015, 25(3):1650-1665. [23] Wang X. F., Tu Z. H., Hu Z. J., Bounded and compact Toeplitz operators with positive measure symbol on Fock-type spaces, J. Geom. Anal., 2020, 30(4):4324-4355. [24] Zhang Y. Y., Wang X. F., Hu Z. J., Toeplitz operators on Bergman spaces with exponential weights, Preprint. [25] Zhu K. H., Operator Theory in Function Spaces, Mathematical Surveys and Monographs, 2nd Edn, American Mathematical Society, Providence, 2007. [26] Zhu K. H., Analysis on Fock Spaces, Springer, New York, 2012.
|
[1] | 黄穗, 王伟. Fock空间上对偶Toeplitz算子的交换性[J]. 数学学报, 2021, 64(4): 579-586. | [2] | 李永宁, 丁宣浩. Hankel算子的乘积与有限秩算子[J]. 数学学报, 2021, 64(3): 493-500. | [3] | 何忠华, 夏锦, 王晓峰. 圆环的加正规权Bergman空间上正符号Toeplitz算子[J]. 数学学报, 2021, 64(3): 353-374. | [4] | 王晓峰, 夏锦, 陈建军. 广义Fock空间上的Hankel算子[J]. 数学学报, 2019, 62(4): 561-572. | [5] | 王晓峰, 夏锦, 陈建军. 广义Segal-Bargmann空间上无界Toeplitz算子的交换[J]. 数学学报, 2019, 62(3): 409-426. | [6] | 秦杰, 刘柚岐, 黄穗. Dirichlet空间上Bergman型Toeplitz算子的代数性质[J]. 数学学报, 2019, 62(3): 449-456. | [7] | 桑元琦, 丁宣浩. 重调和Hardy空间Toeplitz算子的交换性[J]. 数学学报, 2018, 61(4): 577-584. | [8] | 秦杰, 黄穗. Dirichlet空间上的Bergman型Toeplitz算子[J]. 数学学报, 2018, 61(4): 619-624. | [9] | 陈建军, 王晓峰, 夏锦. 有界对称区域上Dirichlet空间中的紧Toeplitz算子[J]. Acta Mathematica Sinica, English Series, 2015, 58(6): 923-934. | [10] | 张阚, 丰雪, 董建国, 关驰, 于妍. 单位球加权Bergman空间上的乘法算子[J]. Acta Mathematica Sinica, English Series, 2015, 58(1): 125-130. | [11] | 王春梅, 于天秋. 一类解析Toeplitz算子的约化子空间[J]. Acta Mathematica Sinica, English Series, 2014, 57(5): 841-850. | [12] | 黄穗, 何艳. Dirichlet空间上的Bergman型Toeplitz算子[J]. Acta Mathematica Sinica, English Series, 2013, 56(6): 951-956. | [13] | 夏锦, 王晓峰, 曹广福. 调和Dirichlet空间上的Toeplitz算子[J]. Acta Mathematica Sinica, English Series, 2013, 56(3): 311-330. | [14] | 何莉, 曹广福, 何忠华. 单位球的加权Bergman空间上具有L1符号的Toeplitz算子[J]. Acta Mathematica Sinica, English Series, 2013, 56(2): 233-244. | [15] | 徐景实, 周放军. 非双倍测度空间上的Toeplitz算子[J]. Acta Mathematica Sinica, English Series, 2012, 55(6): 1001-1012. |
|
PDF全文下载地址:
http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23801
多线性奇异积分交换子的有界性瞿萌,方小珍,王敏安徽师范大学数学与统计学院芜湖241003BoundednessoftheCommutatorsofMultilinearSingularIntegralsMengQU,XiaoZhenFANG,MinWANGSchoolofMathematicsand ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27有界分块算子矩阵的数值半径估计邬慧婷1,吴德玉1,阿拉坦仓21.内蒙古大学数学科学学院呼和浩特010021;2.呼和浩特民族学院呼和浩特010050NumericalRangeEstimationofBlockOperatorMatricesHuiTingWU1,DeYuWU1,Alatancang ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27圆环的加正规权Bergman空间上正符号Toeplitz算子何忠华1,夏锦2,王晓峰21.广东金融学院金融数学与统计学院广州510521;2.广州大学数学与信息科学学院广州510006PositiveToeplitzOperatorsonBergmanSpaceofAnnularInducedbyR ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27Frchet空间上集值微分方程初值问题解的高阶收敛性王培光,邢珍钰,吴曦冉河北大学数学与信息科学学院保定071002Higher-OrderConvergenceofSolutionsofInitialValueProblemforSetDifferentialEquationsin ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27Banach空间中正则非退化异宿环的Lipschitz扰动陈员龙,骆世广广东金融学院金融数学与统计学院广州510521TheLipschitzPerturbationsofRegularNondegenrateHeteroclinicCyclesinBanachSpacesYuanLongCHEN, ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27Hankel算子的乘积与有限秩算子李永宁1,2,丁宣浩1,21.重庆工商大学数学与统计学院重庆400067;2.经济社会应用统计重庆市重点实验室重庆400067TheProductofHankelOperatorsandtheFiniteRankOperatorsYongNingLI1,2,Xuan ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27半序MengerPM-空间中广义弱压缩映射的最佳逼近点定理吴照奇1,朱传喜1,袁成桂21.南昌大学理学院数学系南昌330031;2.英国斯旺西大学数学系斯旺西SA28PPBestProximityPointTheoremsforGeneralizedWeakContractiveMappingsin ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27完备度量空间中的混沌判定吴小英,陈员龙,王芬广东金融学院金融数学与统计学院广州510521ChaoticCriteriainCompleteMetricSpacesXiaoYingWU,YuanLong,CHENFenWANGSchoolofFinancialMathematicsandStatis ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27双截断Baskakov局部化算子的收敛性谢林森1,谢庭藩2,杜鸿11.丽水学院数学系丽水323000;2.中国计量大学应用数学系杭州310018ConvergenceofBi-shiftLocalizedBaskakovOperatorsLinSenXIE1,TingFanXIE2,HongDU11 ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27空间几何常数与集值非扩张映射的不动点左占飞重庆三峡学院数学与统计学院重庆404100SomeGeometricConstantsandFixedPointsforMultivaluedNonexpansiveMappingsZhanFeiZUODepartmentofMathematicsandSt ... 中科院数学与系统科学研究院 本站小编 Free考研考试 2021-12-27
|