论文标题
两种重量不平等的必要条件，用于单数积分算子
Neccessary conditions for two weight inequalities for singular integral operators
论文作者
论文摘要
We prove necessary conditions on pairs of measures $(μ,ν)$ for a singular integral operator $T$ to satisfy weak $(p,p)$ inequalities, $1\leq p<\infty$, provided the kernel of $T$ satisfies a weak non-degeneracy condition first introduced by Stein, and the measure $μ$ satisfies a weak doubling condition related to the non-degeneracy of the kernel.我们还显示了对操作员的$（μ，σ）$对成对的结果$t_σf= t（f \，dσ）$，这在对加权规范不平等的研究中起着重要作用。我们的主要工具是对平均操作员的强类型不平等的仔细分析；这些结果本身就是感兴趣的。最后，作为我们技术的应用，我们表明一般而言，单数操作员不满足端点强型不等式$ t：l^1（ν）\ rightarrow l^1（μ）$。我们的结果统一并扩展了许多已知结果。
We prove necessary conditions on pairs of measures $(μ,ν)$ for a singular integral operator $T$ to satisfy weak $(p,p)$ inequalities, $1\leq p<\infty$, provided the kernel of $T$ satisfies a weak non-degeneracy condition first introduced by Stein, and the measure $μ$ satisfies a weak doubling condition related to the non-degeneracy of the kernel. We also show similar results for pairs of measures $(μ,σ)$ for the operator $T_σf = T(f\,dσ)$, which has come to play an important role in the study of weighted norm inequalities. Our major tool is a careful analysis of the strong type inequalities for averaging operators; these results are of interest in their own right. Finally, as an application of our techniques, we show that in general a singular operator does not satisfy the endpoint strong type inequality $T : L^1(ν) \rightarrow L^1(μ)$. Our results unify and extend a number of known results.
