On a generalization of the H\"{o}rmander condition
On a generalization of the H\"{o}rmander condition
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关于 H"{o}mander 条件的推广
DOI：
10.1090/bproc/125
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Suzuki Soichiro
中科院分区：
文献类型：
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作者：
天野佑紀;Suzuki Soichiro
我们考虑一个自然推广的经典Hörmander条件的Calderón-Zygmund理论。最近作者[J.傅立叶分析。Appl. 27（2021）]证明了奇异积分算子在平均Hörmander条件下的有界性，该条件最初由Grafakos和Stockdale [Bull. Hellenic Math. Soc. 63（2019），pp. 54-63]。在本文中，我们证明了平均条件实际上与经典条件一致。另一方面，我们引入了一个新的变体的Hörmander条件，这是严格弱于经典的，但仍然足够的有界性。此外，它仍然可以在非加倍设置中工作，只需稍加修改。引用
We consider a natural generalization of the classical Hörmander condition in the Calderón–Zygmund theory. Recently the author [J. Fourier Anal. Appl. 27 (2021)] proved theboundedness of singular integral operators under themean Hörmander condition, which was originally introduced by Grafakos and Stockdale [Bull. Hellenic Math. Soc. 63 (2019), pp. 54–63]. In this paper, we show that themean condition actually coincides with the classical one. On the other hand, we introduce a new variant of the Hörmander condition, which is strictly weaker than the classical one but still enough for theboundedness. Moreover, it still works in the non-doubling setting with a little modification. References