Weighted Fractional Differentiation Composition Operators from Mixed-Norm Spaces to Weighted-Type Spaces
Keyword(s):
Let 𝔻 be an open unit disc in the complex plane ℂ and let φ:𝔻→𝔻 as well as u:𝔻→ℂ be analytic maps. For an analytic function f(z)=∑n=0∞anzn on 𝔻 the weighted fractional differentiation composition operator is defined as (Dφ,uβf)(z)=u(z)f[β](φ(z)), where β≥0, f[β](z)=∑n=0∞(Γ(n+1+β)/Γ(n+1))anzn, and f0z=fz. In this paper, we obtain a characterization of boundedness and compactness of weighted fractional differentiation composition operator from mixed-norm space Hp,q,ϕ to weighted-type space Hμ∞.
2018 ◽
Vol 25
(4)
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pp. 555-563
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2009 ◽
Vol 50
(4)
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pp. 726-736
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2016 ◽
Vol 17
(2)
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pp. 303-318
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2019 ◽
Vol 13
(04)
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pp. 2050082