Essential norms of Volterra-type operators between~ZygmundZygmund~ type spaces

~In this paper, we investigate the boundedness of some Volterra-type operators between ~$Zygmund$~ type spaces. Then, we give the essential norms of such operators in terms of ~$g,\varphi$, their derivatives and the n-th power ~$\varphi^n$ of ~$\varphi$

Volterra operators and semigroups in weighted Banach spaces of analytic functions

We characterize the boundedness, compactness and weak compactness of Volterra operators Vg( f )(z) := z 0 f (ζ )g (ζ ) dζ acting between different weighted spaces of type H∞ v in terms of the symbol function g, for the case when v is a quasi-normal weight, a notion weaker than normality. Then we apply the characterization of compactness to analyze the behavior of semigroups of composition operators on H∞ v

Generalized integral type Hilbert operator acting on weighted Bloch space

Let $\mu$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $$\mathcal{I}_{\mu_{\alpha+1}}(f)(z)=\int_{0}^{1}\frac{f(t)}{(1-tz)^{\alpha+1}}d\mu(t)\ \ \ (\alpha>-1).$$ The operator $\mathcal{I}_{\mu_{1}}$ has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of $\mathcal{I}_{\mu_{\alpha+1}}$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of $\mathcal{I}_{\mu_{\alpha+1}}$ acting between Bloch type spaces, logarithmic Bloch spaces among others.Comment: arXiv admin note: text overlap with arXiv:2208.1074