On order bounded weighted composition operators between Dirichlet spaces

Sharma, Ajay K.

doi:10.1007/s11117-016-0462-9

Cited by 12 publications

(4 citation statements)

References 9 publications

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“…The Volterra type operator T g was introduced by Pommerenke [25] to study the exponentials of BMOA functions and in the meantime, he proved that T g acting on the Hardy-Hilbert space H 2 is bounded if and only if g ∈ BM OA . After his work, Aleman, Siskakis and Cima [1,26] studied the boundedness and compactness of T g on the Hardy space H p , where they showed that T g is bounded (compact) on H p , 0 < p < ∞, if and only if g ∈ BM OA (g ∈ V M OA). For the related works, see [16].…”

Section: Boundedness Of Volterra Type Operatorsmentioning

confidence: 99%

“…Order boundedness plays an important role in studying the properties of many concrete operators acting between Banach spaces like Hardy spaces, weighted Bergman spaces and so forth (see [13,14,27]). Recently, order boundedness of weighted composition operators between weighted Dirichlet spaces were studied in [9,26] . In this section, we investigate the order boundedness of Volterra type operators between weighted Dirichlet spaces.…”

Section: Order Boundedness Of Volterra Type Operatorsmentioning

confidence: 99%

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Volterra Type Operators Between Bloch Type Spaces and Weighted Banach Spaces

Lin

2019

Integr. Equ. Oper. Theory

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The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Peláez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for the boundedness are not complete. In this paper, we completely characterize the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D p α to D q β (−1 < α, β and 0 < p < q < ∞), which essentially complete their works. Furthermore, we investigate the order boundedness of Volterra type operators between weighted Dirichlet spaces.2010 Mathematics Subject Classification. 47G10, 31C25, 47B38.

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Section: Boundedness Of Volterra Type Operatorsmentioning

confidence: 99%

Section: Order Boundedness Of Volterra Type Operatorsmentioning

confidence: 99%

Volterra Type Operators Between Bloch Type Spaces and Weighted Banach Spaces

Lin

2019

Integr. Equ. Oper. Theory

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“…Recall that the order boundedness is a property of operators which is closely related to the notion of boundedness (see [6,15]). For the notion of the order boundedness of T :…”

Section: Introductionmentioning

confidence: 99%

Products of Composition, Multiplication and Iterated Differentiation Operators Between Banach Spaces of Holomorphic Functions

Wang¹,

Wang²,

Guo³

2020

Taiwanese J. Math.

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Let H(D) denote the space of holomorphic functions on the unit disk D of C, ψ, ϕ ∈ H(D), ϕ(D) ⊂ D and n ∈ N ∪ {0}. Let C ϕ , M ψ and D n denote the composition, multiplication and iterated differentiation operators, respectively. To treat the operators induced by products of these operators in a unified manner, we introduce a sum operator n j=0 M ψj C ϕ D j . We characterize the boundedness and compactness of this sum operator mapping from a large class of Banach spaces of holomorphic functions into the kth weighted-type space W, and give its estimates of norm and essential norm. Our results show that the boundedness and compactness of the sum operator depend only on the symbols and the norm of the point-evaluation functionals on the domain space. Our results cover many known results in the literature. Moreover, we introduce the order boundedness of the sum operator and turn its study into that of the boundedness and compactness.

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“…Order boundedness of weighted composition operators W φ,ϕ between spaces D p p−1 and D q q−1 were studied in [8,22] . In this paper, we first extend their results to weighted composition operators between acting between different weighted Dirichlet spaces which cover all cases.…”

Section: Introductionmentioning

confidence: 99%

Order boundedness of weighted composition operators on weighted Dirichlet spaces and derivative Hardy spaces

Lin¹,

Liu²,

Wu³

2019

Preprint

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On order bounded weighted composition operators between Dirichlet spaces

Cited by 12 publications

References 9 publications

Volterra Type Operators Between Bloch Type Spaces and Weighted Banach Spaces

Volterra Type Operators Between Bloch Type Spaces and Weighted Banach Spaces

Products of Composition, Multiplication and Iterated Differentiation Operators Between Banach Spaces of Holomorphic Functions

Order boundedness of weighted composition operators on weighted Dirichlet spaces and derivative Hardy spaces

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