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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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Table of 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 $r\geq2$.