Order bounded weighted composition operators mapping into the dirichlet type spaces

Gao, Yong-Xin; Kumar, Sanjay; Zhou, Zehua

doi:10.1007/s11401-016-0956-6

Cited by 10 publications

(2 citation statements)

References 22 publications

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“…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%

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: 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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“…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%