Essential Norm of Weighted Composition Operators From $$H^\infty $$ to nth Weighted Type Spaces

Weighted composition operators from the Bloch space tonth weighted-typespaces

“…Similar to the proof of Lemma 2.3 in [1], we see that the system (2.5) has a unique solution and the solution is independent of choice a and φ(a) . If c 1 , c 2 , ..., c n is that solution, we get u a (z) = d a,c1,c2,...,cn (z), as desired.…”

“…Let β > 0 and µ(z) = (1 − |z| 2 ) β . The space W 1 µ coincides with the Bloch-type space B β . In particular, B 1 is the classical Bloch space B .…”

The Stević-Sharma operator on the Lipschitz space into the logarithmic Bloch space

“…We refer the interested reader to [7] and [17] for the theory of composition operators and to [6,13,18,20,21] for (weighted) composition on some spaces of analytic functions. For essential norm of (generalized) weighted composition operators from some spaces of analytic functions into nth weighted type spaces, we refer for example to [1,2,14].…”

Weighted Composition Operators from Derivative Hardy Spaces into n -th Weighted-Type Spaces

“…Furthermore, when μ(z) � (1 − |z| 2 ), B μ � B is the Bloch space and Z μ � Z is the Zygmund space. For some results on the space W n μ , see references [2,[8][9][10][11][12][13].…”

“…In [12], Stević studied the boundedness and compactness of weighted composition operators from H ∞ and the Bloch space to W n μ . See references [8][9][10] for more characterizations for weighted composition operators from H ∞ and the Bloch space to W n μ . In [16], Zhu and Du studied the boundedness, compactness, and essential norm of weighted composition operators from weighted Bergman spaces with doubling weight A p ω to W n μ .…”