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).
|Number of pages||7|
|Journal||Far East Journal of Mathematical Sciences|
|Publication status||Published - Oct 2011|
- Carleman formulas
- Cauchy integrals
- Hardy classes