### Abstract

Let α, β be orientation-preserving homeomorphisms of [0,∞] onto itself, which have only two fixed points at 0 and ∞, and whose restrictions to ℝ_{+} = (0,∞) are diffeomorphisms, and let U_{α}, U_{β} be the corresponding isometric shift operators on the space L^{p}(ℝ_{+}) given by (Formula presented) for (Formula presented). We prove sufficient conditions for the right and left Fredholmness on L^{p}(ℝ_{+}) of singular integral operators of the form (Formula presented), where (Formula presented) is a weighted Cauchy singular integral operator, (Formula presented) and (Formula presented) are operators in the Wiener algebras of functional operators with shifts. We assume that the coefficients a_{k}, b_{k} for (Formula presented) and the derivatives of the shifts (Formula presented) are bounded continuous functions on ℝ_{+} which may have slowly oscillating discontinuities at 0 and ∞.

Original language | English |
---|---|

Title of host publication | Operator Theory |

Subtitle of host publication | Advances and Applications |

Publisher | Springer International Publishing |

Pages | 221-246 |

Number of pages | 26 |

Volume | 267 |

DOIs | |

Publication status | Published - 2018 |

### Publication series

Name | Operator Theory: Advances and Applications |
---|---|

Volume | 267 |

ISSN (Print) | 0255-0156 |

ISSN (Electronic) | 2296-4878 |

### Keywords

- Left Fredholmness
- Mellin pseudodifferential operator
- Right Fredholmness
- Slowly oscillating shift
- Weighted singular integral operator
- Wiener algebra of functional operators

## Fingerprint Dive into the research topics of 'Semi-Fredholmness of Weighted Singular Integral Operators with Shifts and Slowly Oscillating Data'. Together they form a unique fingerprint.

## Cite this

*Operator Theory: Advances and Applications*(Vol. 267, pp. 221-246). (Operator Theory: Advances and Applications; Vol. 267). Springer International Publishing. https://doi.org/10.1007/978-3-319-72449-2_11