• Corpus ID: 248377776

Constructions of some families of smooth Cauchy transforms

  title={Constructions of some families of smooth Cauchy transforms},
  author={Adem Limani and Bartosz Malman},
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… 


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