具有临界阶的双参数和双线性卡尔德隆-瓦扬库尔定理

IF 1 3区数学 Q1 MATHEMATICS

Forum Mathematicum Pub Date : 2024-01-30 DOI:10.1515/forum-2023-0458

Jiao Chen, Liang Huang, Guozhen Lu

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引用次数: 0

摘要

本文通过推导符号上的充分必要条件，建立了 L p L^{p} 空间上具有临界阶符号的双参数和双线性伪微分算子的尖锐卡尔德隆-韦朗库尔定理。这使[G. Lu and L. Zhang, Bi-parameter and bilinear Calderón-Vaillancourt theorem with subcritical order, Forum Math.28 2016, 6, 1087-1094]，该结果只证明了亚临界阶的符号。

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Bi-parameter and bilinear Calderón–Vaillancourt theorem with critical order

In this paper, we establish the sharp Calderón–Vaillancourt theorem on L p

L^{p}

spaces for bi-parameter and bilinear pseudo-differential operators with symbols of critical order by deriving a sufficient and necessary condition on its symbol. This sharpens the result of [G. Lu and L. Zhang, Bi-parameter and bilinear Calderón–Vaillancourt theorem with subcritical order, Forum Math. 28 2016, 6, 1087–1094] which was only proved for symbols of subcritical order.

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来源期刊

Forum Mathematicum 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Forum Mathematicum is a general mathematics journal, which is devoted to the publication of research articles in all fields of pure and applied mathematics, including mathematical physics. Forum Mathematicum belongs to the top 50 journals in pure and applied mathematics, as measured by citation impact.