Access the full text.
Sign up today, get DeepDyve free for 14 days.
For functions $$ \mu : {\mathbb {N}}_0 \rightarrow {\mathbb {C}} $$ μ : N 0 → C and $$ \theta : {\mathbb {N}}_0 \rightarrow {\mathbb {N}}_0 $$ θ : N 0 → N 0 , the weighted composition operator is the operator $$ \varGamma _{\mu , \theta }: {\mathcal {H}}_\beta ^p \rightarrow {\mathbb {C}}^{{\mathbb {N}}_0}$$ Γ μ , θ : H β p → C N 0 defined by $$ \varGamma _{\mu , \theta }(x) = \bigl ( \sum _{m=0}^k\mu (k-m) x_{\theta (m)}\bigr )_{k =0}^\infty $$ Γ μ , θ ( x ) = ( ∑ m = 0 k μ ( k - m ) x θ ( m ) ) k = 0 ∞ for all $$ x = (x_k) \in {\mathcal {H}}_\beta ^p $$ x = ( x k ) ∈ H β p . This paper deals with the properties of weighted composition operators on weighted Hardy spaces $$ {\mathcal {H}}_\beta ^p$$ H β p for $$ 1 \le p \le \infty $$ 1 ≤ p ≤ ∞ . The necessary and sufficient conditions are investigated for a weighted composition operator to be compact. A compact subset of non-negative real numbers containing the essential norm of $$ \varGamma _{\mu , \theta } $$ Γ μ , θ on $$ {\mathcal {H}}_\beta ^p$$ H β p is also computed. The condition under which weighted composition operators commute is also explored.
Computational Methods and Function Theory – Springer Journals
Published: Jun 17, 2019
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.