Local cone multipliers and Cauchy–Szegö projections in bounded symmetric domains

IF 1 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2024-09-12 DOI:10.1112/jlms.12986

Fernando Ballesta Yagüe, Gustavo Garrigós

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Abstract

We show that the cone multiplier satisfies local $L^{p}$ - $L^{q}$ bounds only in the trivial range $1 ⩽ q ⩽ 2 ⩽ p ⩽ \infty$ . To do so, we suitably adapt to this setting the proof of Fefferman for the ball multiplier. As a consequence we answer negatively a question by Békollé and Bonami, regarding the continuity from $L^{p} \to L^{q}$ of the Cauchy–Szegö projections associated with a class of bounded symmetric domains in $C^{n}$ with rank $r ⩾ 2$ .

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有界对称域中的局部锥乘数和考奇-塞格投影

我们证明，锥乘法器仅在微不足道的范围 1 ⩽ q ⩽ 2 ⩽ p ⩽ ∞ 1\leqslant q\leqslant 2\leqslant p\leqslant \infty$ 中满足局部 L p $L^p$ - L q $L^q$ 约束。为此，我们把费弗曼对球乘法器的证明适当地调整到这个环境中。因此，我们否定地回答了贝科雷和博纳米提出的一个问题，即从 L p → L q $L^p\rightarrow L^q$ 与 C n 中一类秩为 r ⩾ 2 $r\geqslant 2$ 的有界对称域相关的考奇-塞戈投影的连续性问题。

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.