## Abstract

For any Calderón-Zygmund operator T the following sharp estimate is obtained for 1 p <∞ ||T|| Lp(ω)≤CVp||ω|| A_{1}, where v_{p} = p^{2}/p-1log(e+1/p-1). In the case where p=2 and T is a classical convolution singular integral, this result is due to R. Fefferman and J. Fipher [7]. Then, we deduce the following weak type (1,1) estimate related to a problem of Muckenhoupt and Wheeden [11]: sup λω{x ∈^{n} : |Tf(x)>λ} ≤cφ(||ω ||A_{1})&R^{n}|f|ω dx, λ>0 where w ∈ A^{1} andψ(t)=t(1+log^{+}t(1+log^{+}log^{+} t).

Original language | English |
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Article number | rnm161 |

Journal | International Mathematics Research Notices |

Volume | 2008 |

Issue number | 1 |

DOIs | |

State | Published - 2008 |

Externally published | Yes |

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