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Zygmund空间上的微分复合算子
Composition Followed by Differentiation on the Zygmund Space
讨论 Zygmund空间Z = {f ∈H(D): supz∈D(1-|z|2)|f" (z)|< ∞}上的微分复合算子DCφ, 这里Cφ 是复合算子, D 是微分算子. 得到了 DCφ 在 Zygmund空间 Z 和小 Zygmund 空间 Z0上是有界算子与紧算子的充分必要条件.
We consider linear product operator DCφ acting on the Zygmund space Z = {f ∈H(D) : supz∈D(1-|z|2)|f" (z)|< ∞}, where Cφ is the composition operator and D is the differentiation operator. The boundedness and compactness of the operator DCφ on the Zygmund space Z and the little Zygmund space Z0 are established in terms of the function theorectic property of the symbol φ.
Zygmund空间 / 微分算子 / 复合算子 / 有界性 / 紧性 {{custom_keyword}} /
Zygmund space / differentiation operator / composition operator {{custom_keyword}} /
[1] Cowen C. C., Maccluer B. D., Composition Operator on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995.
[2] Duren P., Theory of Hp Spaces, Academic Press, New York, 1970.
[3] Hibschweiler R. A., Portnoy N., Composition followed by differentiation between Bergman and Hardy spaces, Rocky Mountain Math., 2005, 35(3): 843-855.
[4] Li S., Stevi? S., Gerneralized composition operators on the Zygmund spaces and Bloch type spaces, J. Math. Anal. Appl., 2008, 338(2): 1282-1295.
[5] Li S., Stevi? S., Products of Volterra type operator and composition operator from H∞ and Bloch spaces to Zygmund spaces, J. Math Anal. Appl., 2008, 345(1): 40-52.
[6] Li S., Stevi? S., Weighted composition operators from Zygmund spaces into Bloch spaces, Appl. Math. Comput., 2008, 206(2): 825-831.
[7] Liu Y., Yu Y., Composition followed by differentiation between H∞ and Zygmund spaces, Complex. Anal. Oper. Theory, 2012, 6(1): 121-137.
[8] Madigan K., Composition operators on analytic Lipschitz spaces, Proc. Amer. Math. Soc., 1993, 119(2): 465-473.
[9] Madigan K., Matheson A., Compact composition operators on the Bloch space, Trans. Amer. Math. Soc., 1995, 347(7): 2679-2687.
[10] Ohno S., Products of composition and differentiation between Hardy spaces, Bull. Austral. Math. Soc., 2006, 73(2): 235-243.
[11] Ohno S., Stroethoff K., Zhao R., Weighted composition operators between Bloch-type spaces, Rocky Mountain J. Math., 2003, 33(1): 191-215.
[12] Ohno S., Zhao R., Weighted composition operators on the Bloch space, Bull. Austral. Math. Soc., 2001, 63(2): 177-185.
[13] Smith W., Composition operators between Bergman and Hardy spaces, Trans. Amer. Math. Soc., 1996, 348(6): 2331-2348.
[14] Ye S. L., Norm and essential norm of composition followed by differentiation from logarithmic Bloch spaces to H∞μ, Abstr. Appl. Anal., 2014, 2014, Article ID 725145; 6 pages.
[15] Ye S. L., A weighted composition operator on the logarithmic Bloch space, Bull. Korean Math. Soc., 2010, 47(3): 527-540.
[16] Ye S. L., Weighted composition operator between the α-Bloch spaces and the little logarithmic Bloch, J. Comput. Anal. Appl., 2009, 11(3): 443-450.
[17] Ye S. L., A weighted composition operator between different weighted Bloch-type spaces, Acta Math. Sinica, Chin. Ser., 2007, 50(4): 927-942.
[18] Ye S. L., Hu Q., Weighted composition operators on the Zygmund space, Abstr. Appl. Anal., 2012, 2012: Article ID 462482, 18 pages.
[19] Ye S. L., Zhuo Z., Weighted composition operators from Hardy to Zygmund type spaces, Abstr. Appl. Anal., 2013, 2013: Article ID 365286, 10 pages.
[20] Zhu K., Bloch type spaces of analytic functions, Rocky Mountain J. Math., 1993, 23(3): 1143-1177.
[21] Zygmund A., Trigonometric Series, Cambridge University Press, Cambridge, 1959.
福建省自然科学基金资助项目(2015J01005)及省属高校专项基金资助项目(JK2012010)
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