On a Stević–Sharma Operator from Hardy Spaces to Zygmund-Type Spaces on the Unit Disk

Zhang, Fang; Liu, Yongmin

doi:10.1007/s11785-016-0578-8

Cited by 21 publications

(9 citation statements)

References 42 publications

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“…Remark 16. Putting n = 2ðμðzÞ = ð1 − jzj 2 Þ a Þ in Theorems 6, 7, 8, and 9 and Corollaries 12 and 13 and applying (65), similar results are achieved for operator T m u,v,φ : H p ⟶ Z μ ðT m u,v,φ : H p ⟶ Z α Þ (generalizing Theorems 7 and 9 [10]).…”

Section: Corollary 12mentioning

confidence: 56%

“…Product-type operators on some spaces of analytic functions on the unit disc have become a subject of increasing interest in the recent years. We refer the reader to [6][7][8][9][10] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…Liu and Yu have considered boundedness and compactness of operator T 0 u,v,φ from Hardy spaces and H ∞ into the logarithmic Bloch space in [11,12]. Also, Zhang and Liu have found some characterizations for boundedness and compactness of operator T 0 u,v,φ from Hardy spaces into the weighted Zygmund space in [10]. Recently, the boundedness, compactness, and norm of operator T 0 u,v,φ : H p ⟶ W n μ are considered in [13].…”

Section: Introductionmentioning

confidence: 99%

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The Product-Type Operators from Hardy Spaces into $n$ th Weighted-Type Spaces

Abbasi

2021

Abstract and Applied Analysis

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The main goal of this paper is to investigate the boundedness and essential norm of a class of product-type operators T u , v , φ m , m ∈ ℕ from Hardy spaces into n th weighted-type spaces. As a corollary, we obtain some equivalent conditions for compactness of such operators.

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Section: Corollary 12mentioning

confidence: 56%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Product-Type Operators from Hardy Spaces into $n$ th Weighted-Type Spaces

Abbasi

2021

Abstract and Applied Analysis

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“…A recent study of several operators on Zygmund-type spaces has attracted significant research attention; see, for example, [3][4][5].…”

Section: Introductionmentioning

confidence: 99%

On Stević-Sharma Operators from General Class of Analytic Function Spaces into Zygmund-Type Spaces

Bakhit

Kamal

2022

Journal of Function Spaces

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A Stevi c ′ -Sharma operator denoted by T ψ 1 , ψ 2 , φ is a generalization product of multiplication, differentiation, and composition operators. In this paper, we characterize the bounded and compact Stevi c ′ -Sharma operator T ψ 1 , ψ 2 , φ from a general class X of Banach function spaces into Zygmund-type spaces with some of the most convenient test functions on the open unit disk. Using several restrictive terms, we show that all bounded operators T ψ 1 , ψ 2 , φ from X into the little Zygmund-type spaces are compact. As an application, we show that our results hold up for some other domain spaces of T ψ 1 , ψ 2 , φ , such as the Hardy space and the weighted Bergman space.

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“…Zhu [23] studied the boundedness and compactness of linear operators which are obtained by taking products of multiplication, composition, and differentiation operators from Bergman-type spaces to Berstype spaces. Quite recently, Zhang and Liu [24] presented the boundedness and compactness of the operator T u 1 ,u 2 ,φ from Hardy spaces to Zygmund-type spaces. Liu and Yu [25] gave the complete characterizations for the boundedness and compactness of the operator T u 1 ,u 2 ,φ from Hardy spaces to the logarithmic Bloch spaces.…”

Section: Introductionmentioning

confidence: 99%