Weak type (1, 1) bounds for rough operators, II.
Weak type (1, 1) bounds for rough operators, II.
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DOI：
10.1007/bf01393693
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发表时间：
1988-02
影响因子：
3.1
通讯作者：
Michael Chist;J. R. D. Francia
中科院分区：
文献类型：
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作者：
Michael Chist;J. R. D. Francia
近年来，人们对各种与 Calder-6n 和 Zygmund 奇异积分有关的算子进行了研究，但缺乏经典理论所需的平滑性。通过精炼的L 2 参数和粗略的L p 结果插值，获得了1< p<~ 的L p 有界性。然而，在 Calder6n 和 Zygmund 的原始方法中，奇异积分算子被证明是弱类型 (1, 1)，这一性质在理论中发挥了基础作用。因此，很自然地会问，它们的更奇异的亲戚是否也是弱类型 (1, 1)。肯定的答案将使目前已知的理论更加清晰。在本文中，这样的结果是针对特定类别的运算符获得的。
In recent years a variety of operators related to the singular integrals for Calder-6n and Zygmund, but lacking the smoothness required in the classical theory, have been studied. By means of refined L 2 arguments and interpolation with cruder L p results, the L p boundedness has been obtained for 1< p<~. However in the original approach of Calder6n and Zygmund, singular integral operators were shown to be of weak type (1, 1), a property which played a fundamental role in the theory. Thus it is natural to ask whether their more singular relatives are also of weak type (1, 1). An affirmative answer would sharpen the theory currently known. In the present paper such a result is obtained for a particular class of operators.