Correction and Remark to "Continuity of the mean values of BMO functions and Calderon-Zygmund properties of certain singular integrals"

Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics Pub Date : 1984-05-31 DOI:10.5036/BFSIU1968.16.53

K. Yabuta

引用次数: 1

Abstract

These are singular integrals of Calderon type, related to the Cauchy integral. Then, quite recently, Murai [2] has shown that T1 and T2 are bounded on L2(R). On the other hand, as in our former paper [3], one can easily check that the kernels in the above singular integrals satisfy the desired conditions (3.1), (3.2) and (3.3) in [3]. Hence they are Calderon-Zygmund singular integral operators. Finally we note that, because of the Calderon-Zygmund property, weighted norm inequalities hold for them, i.e., if 1

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对“BMO函数均值的连续性和某些奇异积分的Calderon-Zygmund性质”的修正和注释

这些是卡尔德隆型的奇异积分，与柯西积分有关。最近，Murai[2]证明了T1和T2在L2(R)上有界。另一方面，与我们之前的论文[3]一样，我们可以很容易地检查上述奇异积分中的核满足[3]中的(3.1)、(3.2)和(3.3)所需条件。因此它们是Calderon-Zygmund奇异积分算子。最后我们注意到，由于Calderon-Zygmund性质，它们的加权范数不等式成立，即如果1

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bulletin of The Faculty of Science, Ibaraki University. Series A, Mathematics

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