AN A_p-A_oo INEQUALITY FOR THE HILBERT TRANSFORM

摘要

We prove in particular that for the Hilbert transform, for 1 < ∞ and a weight w ∈ A_p, that we have the inequality ||H||_(Lρ(ω)→Lρ(ω) less, similar||ω||A_ρ1/ρ max{||ω||A∞1/ρ',||ω~(ρ'+1)||A∞1/ρ}The case of ρ=2 is an instance of a recent result of Hyt?nen-Perez, and as a corollary we obtain the well-known bound of S. Petermichl of ||ω||A_ρmax{1,(ρ-1)~(-1)}. This supports a conjectural inequality valid for all Calderón-Zygmund operators T, and ρ≠2.