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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.17997 |
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| _version_ | 1866917766978600960 |
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| author | Yagüe, Fernando Ballesta Garrigós, Gustavo |
| author_facet | Yagüe, Fernando Ballesta Garrigós, Gustavo |
| contents | We show that the cone multiplier satisfies local $L^p$-$L^q$ bounds only in the trivial range $1\leq q\leq 2\leq p\leq\infty$. 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 (Colloq. Math. 68, 1995, 81-100), regarding the continuity from $L^p\to L^q$ of the Cauchy-Szegö projections associated with a class of bounded symmetric domains in $\mathbb{C}^n$ with rank $r\geq2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17997 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local cone multipliers and Cauchy-Szego projections in bounded symmetric domains Yagüe, Fernando Ballesta Garrigós, Gustavo Analysis of PDEs We show that the cone multiplier satisfies local $L^p$-$L^q$ bounds only in the trivial range $1\leq q\leq 2\leq p\leq\infty$. 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 (Colloq. Math. 68, 1995, 81-100), regarding the continuity from $L^p\to L^q$ of the Cauchy-Szegö projections associated with a class of bounded symmetric domains in $\mathbb{C}^n$ with rank $r\geq2$. |
| title | Local cone multipliers and Cauchy-Szego projections in bounded symmetric domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2405.17997 |