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Corpus ID: 248377776

Constructions of some families of smooth Cauchy transforms

@inproceedings{Limani2021ConstructionsOS,
title={Constructions of some families of smooth Cauchy transforms},
author={Adem Limani and Bartosz Malman},
year={2021}
}

For a given Beurling-Carleson subset E of the unit circle T which has positive Lebesgue measure, we give explicit formulas for measurable functions supported on E such that their Cauchy transforms have smooth extensions from D to T . The existence of such functions has been previously established by Khrushchev in 1978, in non-constructive ways by the use of duality arguments. We construct several particular families of such Cauchy transforms with a few applications in operator and function… Expand

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Preface 16. The spaces M(A) and H(A) 17. Hilbert spaces inside H2 18. The structure of H(b) and H(bI ) 19. Geometric representation of H(b) spaces 20. Representation theorems for H(b) and H(bI ) 21.… Expand