### 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 |
---|---|

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 |

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### Keywords

- Carleman formulas
- Cauchy integrals
- Hardy classes

### Cite this

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*Far East Journal of Mathematical Sciences*, vol. 57, no. 1, pp. 105-111.

**Characterization of the 'near H
1' class of functions, using a generalized Cauchy-type integral.** / Chailos, George.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Characterization of the 'near H 1' class of functions, using a generalized Cauchy-type integral

AU - Chailos, George

PY - 2011/10

Y1 - 2011/10

N2 - 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).

AB - 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).

KW - Carleman formulas

KW - Cauchy integrals

KW - Hardy classes

UR - http://www.scopus.com/inward/record.url?scp=80053039284&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:80053039284

VL - 57

SP - 105

EP - 111

JO - Far East Journal of Mathematical Sciences

JF - Far East Journal of Mathematical Sciences

SN - 0972-0871

IS - 1

ER -