## Extended Cesàro operators between different Hardy spaces.(English)Zbl 1163.32004

Summary: Let $$H^p$$ denote the Hardy space of holomorphic functions on the unit ball $$\mathbb B$$.
This note gives some sufficient and necessary conditions for the boundedness and compactness of the following extended Cesàro operators
$T_gf(z)=\int^1_0 f(tz) \operatorname{Re} g(tz) \frac{dt}{t}\quad\text{and}\quad L_gf(z)= \int^1_0 \operatorname{Re} f(tz) g(tz) \frac{dt}{t}\,,$
where $$z\in\mathbb B$$ and $$g$$ is a fixed holomorphic map on $$\mathbb B$$, acting from the space $$H^p$$ into the space $$H^q$$, for the case $$p<q$$.
Our results extend and simplify some one-dimensional results.

### MSC:

 32A35 $$H^p$$-spaces, Nevanlinna spaces of functions in several complex variables
Full Text:

### References:

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