对 F. Chiarenza 和 M. Frasca 论文的评论

IF 0.8 3区数学 Q2 MATHEMATICS Proceedings of the American Mathematical Society Pub Date : 2024-04-19 DOI:10.1090/proc/16885

N. Krylov

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引用次数: 0

摘要

1990 年，F. Chiarenza 和 M. Frasca 发表论文，将 C. Fefferman 关于 p > 1 p>1 时通过 | D u | p |Du|^{p} 的积分来估计 | b u | p |bu|^{p} 的积分的结果加以推广。形式上，他们的证明仅对 d ≥ 3 d\geq 3 有效。我们在这里用一个不同的证明来进一步概括，在这个证明中，对于任何维度 d ≥ 2 d\geq 2，D D 被替换为拉普拉奇的分数幂。

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A remark on a paper by F. Chiarenza and M. Frasca

In 1990 F. Chiarenza and M. Frasca published a paper in which they generalized a result of C. Fefferman on estimates of the integral of | b u | p |bu|^{p} through the integral of | D u | p |Du|^{p} for p > 1 p>1 . Formally their proof is valid only for d ≥ 3 d\geq 3 . We present here further generalization with a different proof in which D D is replaced with the fractional power of the Laplacian for any dimension d ≥ 2 d\geq 2 .

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来源期刊

Proceedings of the American Mathematical Society 数学-数学

CiteScore

1.70

自引率

10.00%

发文量

207

审稿时长

2-4 weeks

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