## Sammanfattning

Let (Formula presented.) denote the space of (Formula presented.)-valued analytic functions (Formula presented.) for which the Hankel operator (Formula presented.) is (Formula presented.)-bounded. Obtaining concrete characterizations of (Formula presented.) has proven to be notoriously hard. Let (Formula presented.) denote fractional differentiation. Motivated originally by control theory, we characterize (Formula presented.)-boundedness of (Formula presented.), where (Formula presented.), in terms of a natural anti-analytic Carleson embedding condition. We obtain three notable corollaries: The first is that (Formula presented.) is not characterized by said embedding condition. The second is that when we add an adjoint embedding condition, we obtain a sufficient but not necessary condition for boundedness of (Formula presented.). The third is that there exists a bounded analytic function for which the associated anti-analytic Carleson embedding is unbounded. As a consequence, boundedness of an analytic Carleson embedding does not imply that the anti-analytic ditto is bounded. This answers a question by Nazarov, Pisier, Treil, and Volberg.

Originalspråk | engelska |
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Sidor (från-till) | 427-451 |

Tidskrift | Geometric and Functional Analysis |

Volym | 27 |

Utgåva | 2 |

Tidigt onlinedatum | 2017 mar 7 |

DOI | |

Status | Published - 2017 apr |

## Ämnesklassifikation (UKÄ)

- Geometri