Characterization of the 'near H 1' class of functions, using a generalized Cauchy-type integral

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Abstract

We set D to be a simply connected domain and we assume that D has a Jordan rectifiable boundary ∂D, and M ⊂ ∂D to be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂D). We provide a characterization of N H 1 M (D), which is the class of holomorphic functions in D which are represented by Carleman formulae on M ⊂ ∂D, via a generalized Cauchy-type integral. Furthermore, we show that this Cauchy-type integral associated to f ∈ N H 1 M(D) is an element of N H 1 M (D).

Original languageEnglish
Pages (from-to)105-111
Number of pages7
JournalFar East Journal of Mathematical Sciences
Volume57
Issue number1
Publication statusPublished - Oct 2011

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Cauchy-type Integral
Lebesgue Measure
Analytic function
Arc of a curve
Class

Keywords

  • Carleman formulas
  • Cauchy integrals
  • Hardy classes

Cite this

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abstract = "We set D to be a simply connected domain and we assume that D has a Jordan rectifiable boundary ∂D, and M ⊂ ∂D to be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂D). We provide a characterization of N H 1 M (D), which is the class of holomorphic functions in D which are represented by Carleman formulae on M ⊂ ∂D, via a generalized Cauchy-type integral. Furthermore, we show that this Cauchy-type integral associated to f ∈ N H 1 M(D) is an element of N H 1 M (D).",
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