## Abstract

Let d ≥ 2 and let η : R^{d - 1} → R be a smooth function which is supported in [- 1, 1]^{d - 1}. Suppose μ is the measure on R^{d} given byμ (E) = under(∫, R^{d - 1}) χ_{E} (x, φ (x)) η (x) d x with φ (x) = ∑_{i = 1}^{d - 1} ± | x_{i} |^{ai}, 1 ≠ a_{i} ∈ R. In this paper we study the L^{p}-L^{q} estimates for singular fractional integral operators given byA f (x) = under(∫, R^{d}) f (x - y) (underover(∏, i = 1, d - 1) | y_{i} |^{γi - 1}) d μ (y) with 0 < γ_{i}.

Original language | English |
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Pages (from-to) | 407-417 |

Number of pages | 11 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 332 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2007 Aug 1 |

Externally published | Yes |

## Keywords

- Fractional integral operator

## ASJC Scopus subject areas

- Analysis
- Applied Mathematics

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