论文标题
现代单数积分理论具有轻度内核规律性
Modern singular integral theory with mild kernel regularity
论文作者
论文摘要
我们提出了一个基于修改的二元转移的框架，以证明在轻度内核规律性下的现代单数积分理论的多个结果。使用新的优化表示定理，我们首先是Figiel的结果，这是针对线性calderón-Zygmund运算符的UMD扩展，具有温和的核规则性，并将我们的新证明扩展到多线性设置，以改善最近的UMD值估计的多线性单数积分的UMD值估计值。接下来，我们开发具有修改后的DINI型假设的多线性奇异积分的产品空间理论，并使用该理论证明双参数加权估计值和两重量换向器估计值。
We present a framework based on modified dyadic shifts to prove multiple results of modern singular integral theory under mild kernel regularity. Using new optimized representation theorems we first revisit a result of Figiel concerning the UMD-extensions of linear Calderón-Zygmund operators with mild kernel regularity and extend our new proof to the multilinear setting improving recent UMD-valued estimates of multilinear singular integrals. Next, we develop the product space theory of the multilinear singular integrals with modified Dini-type assumptions, and use this theory to prove bi-parameter weighted estimates and two-weight commutator estimates.
