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
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