## Composition operators on weighted Hardy spaces.(English)Zbl 1085.47031

The paper is concerned with composition operators on weighted Hardy spaces of the type $$H^p(\beta)=\{f(z)=\sum a_nz^n: \| f\| ^p_\beta:=\sum| a_n| ^p\beta(n)^p<\infty\}$$. Unfortunately, the paper contains some erroneous statements; in particular, not every composition operator $$f\mapsto f\circ \phi$$ maps $$H^p(\beta)$$ into itself. Also, the range of $$p$$ has to exclude $$p=1$$ in order that some statements and formulas make sense. No examples are given as to whether there really exist compact composition operators $$C_\phi$$ on $$H^p(\beta)$$ for the weights appearing in Theorem 1 and for which $$\phi$$ actually has a finite angular derivative at some point.

### MSC:

 47B33 Linear composition operators 47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)