عملگر استویچ شارما از فضای بسوف به فضای زیگموند

نوع مقاله : مقاله پژوهشی

نویسندگان

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

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

چکیده

فرض کنید

$H(mathbb{D})‎$‎‎‎‎‎‎

مجموعه تمام توابع تحلیلی روی‎‎

‎$mathbb{D}$‏،

‎ $u,vin H(mathbb{D})‎$

و تابع تحلیلی

$‎psi‎$‎‎

یک‎‎ خودنگاشت

‎‎‎‎$‎(‎psi(mathbb{D}‎)subset ‎mathbb{‎D}‎‎)‎$‎‎

باشد.

عملگر استویچ شارما

$T_{u,v,psi}‎$‎‎

به‌صورت زیر تعریف می‌شود

‎begin{align*}‎

‎T_{u‎, ‎v‎, ‎psi}f(z) = u(z) f{(psi(z))}‎+ ‎v(z) f'(psi(z))‎ ,‎quad fin H(mathbb{D} )‎, ‎quad zin mathbb{D}‎.

‎end{align*}‎‎

‎‎در این مقاله کرانداری و فشردگی عملگراستویچ شارما را از فضای بسوف به فضای زیگموند مورد بررسی‎ قرار می‌دهیم و شرط‎‌های معادلی برای کرانداری و فشردگی عملگر مذکور ارائه خواهیم داد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Stevi' c-Sharma ‎type ‎‎operator ‎from Besov space into Zygmund space

نویسندگان [English]

  • Ebrahim Abbasi 1
  • Sepide Nasresfahani 2
  • Kamal Khalilpour 1
1 Department of Mathematics, Mahabad Branch, Islamic Azad University, Mahabad, Iran
2 Department of Mathematics, University of Isfahan, Isfahanو Iran.
چکیده [English]

Let‎ $H(mathbb{D})‎$ ‎be ‎the ‎space ‎of ‎all ‎analytic ‎functions ‎on‎ ‎$mathbb{D}‎$. ‎For ‎‎$‎u,vin H(mathbb{D})‎$ ‎and ‎self-map ‎‎$‎psi‎(‎psi(mathbb{D}‎)subset ‎mathbb{‎D}‎‎)‎$‎‎‎ the‎ Stevi' c-Sharma ‎type ‎operator ‎is ‎defined ‎as ‎follows‎

‎begin{align*}‎

‎T_{u‎, ‎v‎, ‎psi}f(z) = u(z) f{(psi(z))}‎+ ‎v(z) f'(psi(z))‎ ,‎quad fin H(mathbb{D} )‎, ‎quad zin mathbb{D}‎.

‎end{align*‎}‎

‎In ‎this ‎paper, ‎we ‎study ‎boundedness ‎and ‎compactness ‎of‎ Stevi' c-Sharma ‎type ‎‎operator ‎from Besov space into Zygmund ‎space ‎and ‎we ‎obtain ‎some ‎equivalence ‎conditions ‎for‎ boundedness ‎and ‎compactness ‎of ‎such ‎operator.

کلیدواژه‌ها [English]

  • Boundedness&lrm
  • Compactness&lrm
  • Besov &lrm
  • space&lrm
  • Zygmund Space
  • &lrm
  • Stevi'
  • c-Sharma &lrm
  • type &lrm
  • operator
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