Geodesic
Product-type operators acting between Dirichlet and Zygmund-type spaces
Filomat, Tome 36 (2022) no. 18, p. 6051

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DOI

Let D = {z ∈ C : |z| 1} be the open unit disk in the complex plane C. By H(D), denote the space of all holomorphic functions on D. For an analytic self map φ on D and u, v ∈ H(D), we have a product type operator T u,v,φ defined by T u,v,φ f (z) = u(z) f (φ(z)) + v(z) f ′ (φ(z)), f ∈ H(D), z ∈ D, This operator is basically a combination of three other operators namely composition operator, multiplication operator and differentiation operator. We study the boundedness and compactness of this operator from Dirichlet-type spaces to Zygmund-type spaces.
DOI : 10.2298/FIL2218051R
Classification : 47B33, 47B37, 33A37, 47B38
Keywords: Zygmund-type spaces, Dirichlet type spaces, product-type operators, boundedness, compactness 
Kuldip Raj; Manisha Devi; M Mursaleen. Product-type operators acting between Dirichlet and Zygmund-type spaces. Filomat, Tome 36 (2022) no. 18, p. 6051 . doi: 10.2298/FIL2218051R
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     title = {Product-type operators acting between {Dirichlet} and {Zygmund-type} spaces},
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     year = {2022},
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     doi = {10.2298/FIL2218051R},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2218051R/}
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