## Abstract

Let ψ:[0, 1]→[0, ∞), s:[0,1]→R be measurable functions and Γ be a parameter curve in Rn given by (t,x)∈[0,1]×Rn→s(t,x)=s(t)x. In this paper, we study a new weighted Hardy-Cesàro operator defined by Uψ,sf(x)=∫01f(s(t)x)ψ(t)dt, for measurable complex-valued functions f on Rn. Under certain conditions on s(t) and on an absolutely homogeneous weight function ω, we characterize the weight function ψ such that U
_{ψ,s} is bounded on weighted Morrey spaces L
^{p,λ}(ω) and then compute the corresponding operator norm of U
_{ψ,s}. We also give a necessary and sufficient condition on the function ψ, which ensures the boundedness of the commutator of the operator U
_{ψ,s} on L
^{p,λ}(ω) with symbols in BMO(ω).

Original language | English |
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Pages (from-to) | 1025-1035 |

Number of pages | 11 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 412 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2014 |

## Keywords

- Commutator
- Maximal operator
- Weighted BMO space
- Weighted Hardy-Cesàro operator
- Weighted Morrey space