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 language | English |
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Pages (from-to) | 105-111 |
Number of pages | 7 |
Journal | Far East Journal of Mathematical Sciences |
Volume | 57 |
Issue number | 1 |
Publication status | Published - Oct 2011 |
Keywords
- Carleman formulas
- Cauchy integrals
- Hardy classes