Analytic function spaces of l^p type on the unit disc: properties and Cesàro operator

Date

2026-6

Author

Akkuş, Metehan

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We study spaces of analytic functions on the unit disc, whose Taylor series coefficients lie in the weighted sequence spaces $\ell^p_\alpha$, comparing them to classical function spaces such as Hardy spaces, Bergman spaces, and Bergman-Besov spaces. We investigate the relationships between these spaces and analyze how the parameters $p$ and $\alpha$ influence inclusion relations, as well as the convergence and boundary growth of functions belonging to $\ell^p_\alpha$. We then introduce the Ces\`aro operator $C$ and study its action on analytic functions and the spaces $\ell^p_\alpha$. In particular, we establish results concerning the boundedness and compactness of $C$. Finally, we determine the eigenvalues and the spectrum of $C$ on $\ell^p_\alpha$. Although this thesis is to a large part a compilation of known results, it also contains several new results that extend these results.

Subject Keywords

Analytic function spaces, Spaces of type $\ell^p_\alpha$, Inclusions, Boundary growth, Cesàro operator

URI

https://hdl.handle.net/11511/119717

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Graduate School of Natural and Applied Sciences, Thesis