اندازه کارلسون و انواع عملگرهای ترکیبی روی فضاهای از نوع بسوف وزندار بردار مقدار

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی، دانشکده ریاضی و آمار، دانشگاه اصفهان، اصفهان، ایران

2 دانشکده فنی و مهندسی خوی، دانشگاه صنعتی ارومیه، ارومیه، ایران

3 گروه ریاضی، دانشکده علوم پایه، دانشگاه آزاد اسلامی، واحد مهاباد، ایران

چکیده

در این مقاله، عملگر ترکیبی ‎$C_phi$‎ و همچنین عملگرهای‎$C_phi D$‎ و ‎$D C_phi$ (حاصل‌ضرب عملگر ترکیبی و عملگر مشتق) را روی فضاهای بسوف وزن‌دار بردار مقدار ‎$mathcal{B}^p_v(X)$‎ و همچنین فضاهای بسوف وزن‌دار بردار مقدار ضعیف ‎$wmathcal{B}^p_v(X)$‎، به‌ازای فضای باناخ مختلط ‎$X$‎ و ‎$1leq p <2$‎ در نظر می گیریم و شرط های معادلی برای کران‌داری و فشردگی این عملگر ها روی فضاهای مذکور، با استفاده از اندازه کارلسون، به‌دست می‌آوریم.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Carleson measure and composition operators on vector valued weighted Besov type spaces

نویسندگان [English]

  • Sepide Nasresfahani 1
  • Mostafa Hassanlou 2
  • Ebrahim Abbasi 3
1 Department of Pure Mathematics, Faculty of Mathematics and statistics, University of Isfahan, Isfahan, Iran
2 Engineering Faculty of Khoy, Urmia University of Technology, Urmia, Iran
3 Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran
چکیده [English]

‎In this paper we investigate composition operator $C_phi$ and also product of composition and differentiation $C_phi D$ and $D C_phi$ on vector valued weighted Besov type space $mathcal{B}^p_v(X)$ and weak vector valued weighted Besov type space $wmathcal{B}^p_v(X)$ for complex Banach space $X$ and $1leq p<2$ ‎and ‎equivalent ‎conditions ‎for‎‎‎ boundedness and compactness of these operators on such spaces have been obtained using Carleson measure‎.

کلیدواژه‌ها [English]

  • composition operator&lrm
  • product of composition and differentiation&lrm
  • Carleson measure&lrm
  • weak vector valued weighted Besov type spaces&lrm
  • boundedness&lrm
  • &lrm
  • compactness
[1] Arregui J. and Blasco O., Bergman and Bloch spaces of vector-valued functions, Math. Nachr.,
261(262) (2003), 3–22.[2] Blasco O., Operators on weighted Bergman spaces and applications, Duke. Math. J., 66 (1992),443–467.
[3] Cima J. A. and Wogan W. R., A Carleson measure theorem for the Bergman spaces on the ball, J.Operator Theory., 7 (1982), 157–165.
[4] Cowen C. and MacCluer B., Composition operators on spaces of Analytic functions, Studies in
Advanced Mathematics. Boca Raton, CRC Pres, 1995.
[5] Geng L. G., Zhou Z.H. and Dong Z. T., Isometric composition operators on weighted Dirichlet typespaces, J. Inequal App., 23 (2012), 1029–1036.
[6] Gul U., Essential spectra of composition operators on the space of bounded analytic functions, Turk.J. Math., 32 (2008), 475–480.
[7] Hassanlou M., Vaezi H. and Wang M., Weighted composition operators on weak vector-valued
Bergman spaces and Hardy spaces, Banach J. Math. Anal., 9(2) (2015), 35–43.
[8] Hasting W., A Carleson measure theorem for Bergman spaces, Proc. Amer. Math. Soc., 52 (1975)237–241.
[9] Hedenmalm H., Krenblum B. and Zhu K., Theory of Bergman Spaces, New York, Springer, 2000.
[10] Jovovic M. and MacCluer B. D., Composition operator on Dirichlet spaces, Acta. Sci. Math.
(Szeged)., 63 (1997), 229–247.
[11] Kumar S., Weighted composition operators between spaces of Dirichlet type, Rev. Math. Complut.,22(2) (2009), 469–488.
[12] Latilla J., Weakly compact composition operators on vector-valued BMOA, J. Math. Anal., 308
(2005), 730–745.[13] Luecking D., A technique for characterizing Carleson measure on Bergman spaces, Proc. Amer.Math. Soc., 87 (1983), 656–660.
[14] MacCluer B. D., Compact composition operator on Hp(BN), Mich. Math. J., 32 (1985), 237–248.
[15] MacCluer B. D., Composition operators on Sp, Houston. J. Math., 13 (1987), 245–254.
[16] Maccluer B. D. and Shapiro J. H., Angular derivatives and compact composition operators on theHardy and Bergman spaces, Can. J. Math., 38 (1986), 878–906.
[17] Nevanlinna R., Analytic functions, Springer Verlag, New York, 1970.
[18] Shapiro J. H., Composition Operators and Classical Function Theory, Berlin, Springer-Verlag, 1993.[19] Stegenga D. A., Multipliers of the Dirichlet spaces, Illinois. J. Math., 24 (1980), 113–139.
[20] Wang M., Weighted composition operators between Dirichlet spaces, Acta. Math. Sci., 31B(2)
(2011), 671–651.[21] Wolf E., Weighted composition operators between weighted Bergman spaces, Rev. R. Acad. Cien.Series. A. Math., 103(1) (2009, 11–15.
[22] Wu Z. and Yang L., Multipliers between Dirichlet spaces, Integral Equations Operator Theory., 23(4)(1998), 482–492.[23] Zorboska N., Composition operators on weighted Dirichlet spaces. Proc. Amer. Math. Soc., 126(1998), 2013-2023.