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PDF(463 KB)
PDF(463 KB)
解析Sobolev型空间上的算子与算子代数
Operators and Operator Algebras on Analytic Sobolev-Type Spaces
介绍Hardy-Sobolev空间和Fock空间及其算子与算子代数研究方面所做的工作，包括对这两类空间上几类特殊算子有界性、紧性、Fredholm性、指标理论、谱和本性谱、范数和本性范数、Schatten-p类的讨论，以及由它们所生成的C*-代数的研究.
We introduce some work on Hardy-Sobolev spaces and Fock spaces and their operators and operator algebras, including discussing the boundedness, compactness, Fredholmness, index theory, spectrum and essential spectrum, norm and essential norm and Schatten-p class of some special kinds of operators on these two types of space, and studying the corresponding C*-algebra generated by them.
Hardy-Sobolev空间 / Fock空间 / 乘子 / 复合算子 {{custom_keyword}} /
Hardy-Sobolev space / Fock space / multiplier / composition operator {{custom_keyword}} /
[1] Auscher P., Russ E., Tchamitchian P., Hardy-Sobolev spaces on strongly Lipschitz domains of Rn, J. Funct. Anal., 2005, 218:54-109.
[2] Berger C., Coburn L., Toeplitz operators and quantum mechanics, J. Funct. Anal., 1986, 68:273-299.
[3] Berger C., Coburn L., Toeplitz operators on the Segal-Bargmann space, Trans. Amer. Math. Soc., 1987, 301:813-829.
[4] Berger C., Coburn L., Zhu K. H., Toeplitz operators and function theory in n-dimensions, Springer Lect. Notes Math., 1987, 1256:28-35.
[5] Bauer W., Coburn L., Isralowitz J., Heat flow, BMO, and the Compactness of Toeplitz operators, J. Funct. Anal., 2010, 259:57-78.
[6] Bruna J., Ortega J. M., Interpolation along manifolds in Hardy-Sobolev spaces, J. Geom. Anal., 1997, 7(1):17-45.
[7] Bauer W., Lee Y. J., Commuting Toeplitz operators on the Segal-Bargmann space, J. Funct. Anal., 2011, 260(2):460-489.
[8] Bommier-Hato H., Youssfi E. H., Hankel Operators on Weighted Fock Spaces, Integr. Equ. Oper. Theory, 2007, 59:1-17.
[9] Cho H. R., Zhu K. H., Fock-Sobolev spaces and their Carleson measures, J. Funct. Anal., 2012, 263(8):2483-2506.
[10] Cohn W. S., Verbitsky I. E., On the trace inequalities for Hardy-Sobolev functions in the unit ball of Cn, Indiana Univ. Math. J., 1994, 43(4):1079-1097.
[11] Cascante C., Ortega J. M., Carleson measures on spaces of Hardy-Sobolev type, Canad. J. Math., 1995, 47(6):1177-1200.
[12] Cascante C., Ortega J. M., Tangential-exceptional sets for Hardy-Sobolev spaces, Illinios J. Math., 1995, 39(1):68-85.
[13] Cascante C., Ortega J. M., Carleson measures for weighted Hardy-Sobolev spaces, Nagoya Math. J., 2007, 186:29-68.
[14] Cho H. R., Zhu K. H., Holomorphic mean Lipschitz spaces and Hardy-Sobolev spaces on the unit ball, Complex Var. Elliptic Equ., 2012, 57(9):995-1024.
[15] Chen X. M., Hou S. Z., A Beurling-type theorem for the Fock space, Proc. Amer. Math. Soc., 2003, 131(9):2791-2795.
[16] Coburn L., Isralowitz J., Li B., Toeplitz operators with BMO symbols on the Segal-Bargmann space, Trans. Amer. Math. Soc., 2011, 363:3015-3030.
[17] Cao G. F., He L., Hardy-Sobolev spaces and their multipliers, Sci. China Math. Ser. A, 2014, 57(11):2361-2368.
[18] Cao G. F., He L., Fredholmness of Multipliers on Hardy-Sobolev spaces, J. Math. Anal. Appl., 2014, 418(1):1-10.
[19] Duren P. L., Theory of Hp Spaces, Academic Press, New York, 1970.
[20] Duren P. L., Schuster A., Bergman Space, Mathematical Surveys and Monographs, 100. Amer. Math. Soc., Providence, 2004.
[21] Englis M., Guo K., Zhang G. K., Toeplitz and Hankel operators and Dixmier traces on the unit ball of Cn, Proc. Amer. Math. Soc., 2009, 137:3669-3678.
[22] Guo K. Y., Zheng D. C., Invariant subspaces, quasi-invariant subspaces, and Hankel operators, J. Funct. Anal., 2001, 187(2):308-342.
[23] Guo K. Y., Homogeneous quasi-invariant subspaces of the Fock space, J. Aust. Math. Soc., 2003, 75(3):399-407.
[24] Guo K. Y., Hou S. Z., Quasi-invariant subspaces generated by polynomials with nonzero leading terms, Studia Math., 2004, 164(3):231-241.
[25] Guo K. Y., Izuchi K., Composition operators on Fock type spaces, Acta Sci. Math. Szeged, 2008, 74(3-4):807-828.
[26] Hou S. Z., Hu J. Y., The codimension formula on quasi-invariant subspaces of the Fock space, Chinese Ann. Math. Ser. B, 2003, 24(3):343-348.
[27] Hu Z., Lv X., Toeplitz operators from one Fock space to another, Integr. Equ. Oper. Theory, 2011, 70(4):541-559.
[28] He L., Cao G. F., Composition operators on Hardy-sobolev spaces, Indian J. Pure Appl. Math., 2015, 46(3):255-267.
[29] Hu Z., Lv X., Toeplitz Operators on Fock Spaces Fφp, Integr. Equ. Oper. Theory, 2014, 80:33-59.
[30] Isralowitz J., Schatten-p class Hankel operators on the Segal-Bargmann space H2(Cn, dμ) for 0< p < 1, J. Operat. Theor., 2011, 66(1):145-160.
[31] Isralowitz J., Compactness and essential norm problems of operators on generalized Fock spaces, Journal of Operator Theory, 2013, 73(2):281-314.
[32] Isralowitz J., Zhu K. H., Toeplitz operators on the Fock space, Integr. Equ. Oper. Theory, 2010, 66:593-611.
[33] Liu L. Z., Orlitz-Hardy-Sobolev space(in Chinese), Natural Science Journal of Changsha Normal University of Water Resources and Electric Power, 1993, 8(1):10-14.
[34] Lou Z. J., Yang S. Z., An atomic decomposition for the Hardy-Sobolev space, Taiwannese J. Math., 2007, 11(4):1167-1176.
[35] Mateu J., Verdera J., BMO harmonic approximation in the plane and spectral synthesis for Hardy-Sobolev space, Rev. Mat. Iberoamericana, 1988, 4(2):291-318.
[36] Mengestie T., On Toeplitz operators between Fock spaces, Integr. Equ. Oper. Theory, 2014, 78(2):213-224.
[37] Ortega J. M., Fabrega J., Multipliers in Hardy-Sobolev spaces, Integr. Equ. Oper. Theory, 2006, 55:535-560.
[38] Peng L. Z., Hardy-Sobolev space(in Chinese), Journal of Beijing University, 1987:26-41.
[39] Perelomov A. M., Generalized Coherent States and Their Applications, Springer, Berlin, 1986.
[40] Schuster A. P., Varolin D., Toeplitz operators and Carleson measures on generalized Bargmann-Fock spaces, Integr. Equ. Oper. Theory, 2012, 72:363-392.
[41] Schneider G., Hankel operators with antiholomorphic symbols on the Fock space, Proc. Amer. Math. Soc., 2004, 132:2399-2409.
[42] Seip K., Youssfi E. H., Hankel operators on Fock spaces and related Bergman kernel estimates, J. Geom. Anal., 2013, 23:170-201.
[43] Wang X. F., Cao G. F., Zhu K. H., Boundedness and compactness of operators on the Fock space, Integr. Equ. Oper. Theory, 2013, 77(3):355-370.
[44] Wang X. F., Cao G. F., Xia J., Toeplitz operators on Fock-Sobolev spaces withpositive measure symbols, Science China Mathematics, 2014, 57(7):1443-1462.
[45] 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.
[46] Xia J. B., Zheng D. C., Localization and Berezin transform on the Fock space, J. Funct. Anal., 2013, 264:97-117.
[47] Xia J. B., Zheng D. C., Standard deviation and Schatten class Hankel operators on the Segal-Bargman space, Indiana Univ. Math. J., 2004, 53:1381-1399.
[48] Xiao L. H., Wang X. F., Xia J., Schatten-p(0[49] Zhu K. H., Spaces of Holomorphic Functions in the Unit Ball, Springer-Verlag, New York, 2005.
[50] Zhu K. H., Analysis of Fock Spaces, Springer, New York, 2012.
[51] Hu Z., Lu J., Essential Norm of Toeplitz Operators on the Fock Spaces, Integr. Equ. Oper. Theory, 2015, 83(2):197-210.
国家自然科学基金资助项目（11271092，11471084，11501136）
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