### Abstract

In this paper we deal with a scale of reproducing kernel Hilbert spaces H_{2} ^{(n)}, n≥0, which are linear subspaces of the classical Hilbertian Hardy space on the right-hand half-plane C^{+}. They are obtained as ranges of the Laplace transform in extended versions of the Paley-Wiener theorem which involve absolutely continuous functions of higher degree. An explicit integral formula is given for the reproducing kernel K_{z,n} of H_{2} ^{(n)}, from which we can find the estimate ‖K_{z,n}‖∼|z|^{−1/2} for z∈C^{+}. Then composition operators C_{φ}:H_{2} ^{(n)}→H_{2} ^{(n)}, C_{φ}f=f∘φ, on these spaces are discussed, giving some necessary and some sufficient conditions for analytic maps φ:C^{+}→C^{+} to induce bounded composition operators.

Original language | English (US) |
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Article number | 124131 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 489 |

Issue number | 1 |

DOIs | |

State | Published - Sep 1 2020 |

### Keywords

- Analytic Hardy spaces on a half plane
- Composition operators
- Higher absolutely continuous function space
- Laplace transform
- Reproducing kernel

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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## Cite this

*Journal of Mathematical Analysis and Applications*,

*489*(1), [124131]. https://doi.org/10.1016/j.jmaa.2020.124131