### Abstract

The norm of the above-mentioned operator S is computed on the unions of parallel lines or concentric circles. The upper bound is found for its norm on the ellipse. In case of weighted spaces on the unit circle, the exact norm is found for some rational weights, and necessary and sufficient conditions on the weight are established, under which the essential norm of S equals 1.

Original language | English (US) |
---|---|

Pages (from-to) | 68-80 |

Number of pages | 13 |

Journal | Integral Equations and Operator Theory |

Volume | 24 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1996 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

### Cite this

*Integral Equations and Operator Theory*,

*24*(1), 68-80. https://doi.org/10.1007/BF01195485

**Norms of the singular integral operator with Cauchy kernel along certain contours.** / Feldman, Israel; Krupnik, Naum; Spitkovsky, Ilya.

Research output: Contribution to journal › Article

*Integral Equations and Operator Theory*, vol. 24, no. 1, pp. 68-80. https://doi.org/10.1007/BF01195485

}

TY - JOUR

T1 - Norms of the singular integral operator with Cauchy kernel along certain contours

AU - Feldman, Israel

AU - Krupnik, Naum

AU - Spitkovsky, Ilya

PY - 1996/1/1

Y1 - 1996/1/1

N2 - The norm of the above-mentioned operator S is computed on the unions of parallel lines or concentric circles. The upper bound is found for its norm on the ellipse. In case of weighted spaces on the unit circle, the exact norm is found for some rational weights, and necessary and sufficient conditions on the weight are established, under which the essential norm of S equals 1.

AB - The norm of the above-mentioned operator S is computed on the unions of parallel lines or concentric circles. The upper bound is found for its norm on the ellipse. In case of weighted spaces on the unit circle, the exact norm is found for some rational weights, and necessary and sufficient conditions on the weight are established, under which the essential norm of S equals 1.

UR - http://www.scopus.com/inward/record.url?scp=0030451422&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030451422&partnerID=8YFLogxK

U2 - 10.1007/BF01195485

DO - 10.1007/BF01195485

M3 - Article

AN - SCOPUS:0030451422

VL - 24

SP - 68

EP - 80

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

SN - 0378-620X

IS - 1

ER -