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The products of differentiation and composition operators D C φ and C φ D m are defined, respectively, as follows: D C φ f ( z ) = f ′ ( φ ( z ) ) φ ′ ( z ), C φ D m f = f ( m ) ∘ φ, f ∈ H ( D ), m ∈ N. The essential norm of a continuous linear operator T between two normed linear spaces X and Y is its distance from the compact operators.
Now we give the upper estimate for the essential norm.
This paper gives an estimate of the essential norm of.
We also show that if the symbol φ is univalent, then the essential norm of Cφ is comparable to its essential norm on the Bloch space.
Fortunately, Shapiro [5] developed relations between the essential norm of on and the Nevanlinna counting function of, and he obtained a nice essential norm formula of in 1987.
Estimates for the norm and the essential norm of the operator are also given.
An estimate for the essential norm of C φ D m is given.
Moreover, an estimate for the essential norm of C φ D m will be given.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com