Sum of weighted differentiation composition operators on weighted spaces of analytic functions

الموضوعات

علوم بحتة وطبيعية

الملخص

The theory of composition operators, multiplication operators and weighted composition operators on different spaces of functions have been the subject matter of study for the last several decades. In recent years, many authors studied the products of these operators with differentiation operators on various analytic function spaces. Recently, researchers have initiated the study of the following sum operator, which unifies the theory of products of all these operators:TkΨ,ϕf =k∑j=0ψj· f(j)◦ϕ =k∑j=0Djψj,ϕ f, f ∈ H (D), where H (D) denotes the space of analytic functions on the unit disc D, S (D) denotes the set of all analytic self maps of D, Ψ = (ψj)kj=0be such that ψj ∈ H (D) andϕ ∈ S (D).In this thesis, we characterize the boundedness and the compactness of the operators TkΨ,ϕ from weighted Bergman spaces Av,p to weighted-type spaces H∞v(H0v)and weighted Zygmund-type spaces Zw (weighted Bloch-type spaces Bw). Besides characterizing boundedness, completely continuous and compactness of the operatorTkΨ,ϕbetween H∞v(H0v) and H∞w (H0w), we obtain essential norm estimates of TkΨ,ϕ. Also, we obtain the boundedness and compactness of the difference TkΨ −TkΦof differential operators between H∞v(H0v) and H∞w (H0w).As applications of TkΨ,ϕ, besides obtaining the boundedness, compactness and essential norm estimates of the weighted differentiation composition operators Dnψ,ϕ:Bv(B0v) → Bw(B0w), Bv(B0v) → H∞w (H0w), H∞v(H0v) → Bw(B0w), we give new characterizations and new essential norm estimates of these operators Dnψ,ϕ.Besides, giving examples of bounded, unbounded, compact and non-compact operators TkΨ,ϕ, we give examples of unbounded weighted differentiation composition operators Dnψ,ϕ: Av,p → Zw(Bw) such that their sum is bounded and also unbounded(non-compact) differential operators TkΨ: H∞v → H∞w such that their difference is bounded (compact).

روابط وملفات

التعريف والنوع

رقم الوثيقة

fead4bde-4b3e-4f23-98e3-15aed9415c62

رقم العقد

0

نوع الوسائط

Crawler

نوع المحتوى

الرسائل العلمية

صيغة المصدر

رسائل دكتوراة

نوع الملف

pdf text

أسماء الملفات

fead4bde-4b3e-4f23-98e3-15aed9415c62_1.pdf

بيانات النشر

ترجمة العنوان

جمع مؤثرات التراكيب التفاضلي المرجحة في فضاءات الدوال التحليلية

ألقاب المؤلفين

[{"name_ar":"Jasbir S. Manhas ","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"Mohammed Said Mohammed Al-Ghafri","title_ar":"اعداد","title_en":"Preparation"}]

اللغة

English

المصدر والدورية

اسم المصدر

Sum of weighted differentiation composition operators on weighted spaces of analytic functions

المحتوى والصفحات

عدد الصفحات

0

كلمات الباحثين

Functional analysis - Operator theory

إشراف وإعداد

الإشراف

Jasbir S. Manhas

الإعداد

Mohammed Said Mohammed Al-Ghafri

الاقتباسات الببليوغرافية