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| Autori principali: | , , |
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| Natura: | Preprint |
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2025
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| Accesso online: | https://arxiv.org/abs/2504.04137 |
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| _version_ | 1866908302809497600 |
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| author | Dimovski, Pavel Pilipovic, Stevan Prangoski, Bojan |
| author_facet | Dimovski, Pavel Pilipovic, Stevan Prangoski, Bojan |
| contents | We show that every Fourier multiplier with real-valued and positively homogeneous symbol of order 0, supported in a cone whose dual cone has a nonempty interior and such that the average of the positive part is sufficiently larger than the average of the negative part does not preserve the $L^1$- nor the $L^\infty$ regularity and neither the continuity.We also construct wave front sets which measure the microlocal regularity with respect to a large class of Banach spaces. As a consequence of the first part, we argue that one can never construct wave front sets that behave in a natural way and measure the microlocal $L^1$- nor $L^\infty$-regularity and neither the continuity |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04137 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a class of Mikhlin multipliers which do not preserve $L^1$-, $L^\infty$-regularity and continuity Dimovski, Pavel Pilipovic, Stevan Prangoski, Bojan Functional Analysis 42B15 We show that every Fourier multiplier with real-valued and positively homogeneous symbol of order 0, supported in a cone whose dual cone has a nonempty interior and such that the average of the positive part is sufficiently larger than the average of the negative part does not preserve the $L^1$- nor the $L^\infty$ regularity and neither the continuity.We also construct wave front sets which measure the microlocal regularity with respect to a large class of Banach spaces. As a consequence of the first part, we argue that one can never construct wave front sets that behave in a natural way and measure the microlocal $L^1$- nor $L^\infty$-regularity and neither the continuity |
| title | On a class of Mikhlin multipliers which do not preserve $L^1$-, $L^\infty$-regularity and continuity |
| topic | Functional Analysis 42B15 |
| url | https://arxiv.org/abs/2504.04137 |