The Poisson Matrix $\mathbf{A}_2$ characteristic and the 3/2 blow up of the Hilbert transform
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911698313543680 |
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| author | Domelevo, Komla Kakaroumpas, Spyridon Petermichl, Stefanie Treil, Sergei Volberg, Alexander |
| author_facet | Domelevo, Komla Kakaroumpas, Spyridon Petermichl, Stefanie Treil, Sergei Volberg, Alexander |
| contents | Recently the matrix $A_2$ conjecture was disproved. Indeed, the growth of the vector Hilbert transform in the matrix weighted $L^2(W)$ space was shown to be at best a constant multiple of $[W]_{\mathbf{A}_2}^{3/2}$. This bound had previously been established and it was thus proved that it is sharp and the conjectured linear growth cannot be obtained. It is a natural question to see if the $3/2$ power persists if we replace the classical matrix $A_2$ characteristic by the "fattened", larger, so-called matrix Poisson $A_2$ characteristic. We show that the 3/2 power, even in this case, cannot be improved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_19637 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Poisson Matrix $\mathbf{A}_2$ characteristic and the 3/2 blow up of the Hilbert transform Domelevo, Komla Kakaroumpas, Spyridon Petermichl, Stefanie Treil, Sergei Volberg, Alexander Classical Analysis and ODEs Recently the matrix $A_2$ conjecture was disproved. Indeed, the growth of the vector Hilbert transform in the matrix weighted $L^2(W)$ space was shown to be at best a constant multiple of $[W]_{\mathbf{A}_2}^{3/2}$. This bound had previously been established and it was thus proved that it is sharp and the conjectured linear growth cannot be obtained. It is a natural question to see if the $3/2$ power persists if we replace the classical matrix $A_2$ characteristic by the "fattened", larger, so-called matrix Poisson $A_2$ characteristic. We show that the 3/2 power, even in this case, cannot be improved. |
| title | The Poisson Matrix $\mathbf{A}_2$ characteristic and the 3/2 blow up of the Hilbert transform |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2605.19637 |