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arXiv · 2208.11452

Generalized integral type Hilbert operator acting on weighted Bloch space

Pengcheng Tang·Xuejun Zhang
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Abstract

Let $μ$ be a finite Borel measure on $[0,1)$. In this paper, we consider the generalized integral type Hilbert operator $$\mathcal{I}_{μ_{α+1}}(f)(z)=\int_{0}^{1}\frac{f(t)}{(1-tz)^{α+1}}dμ(t)\ \ \ (α>-1).$$ The operator $\mathcal{I}_{μ_{1}}$ has been extensively studied recently. The aim of this paper is to study the boundedness(resp. compactness) of $\mathcal{I}_{μ_{α+1}}$ 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}_{μ_{α+1}}$ acting between Bloch type spaces, logarithmic Bloch spaces among others.

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Pengcheng Tang, Xuejun Zhang. 2022-08-24. Generalized integral type Hilbert operator acting on weighted Bloch space. https://doi.org/10.1002/mma.9572

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