POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES
We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geqslant 3$, $\lim _{t\rightarrow 0}e^{it\unicode[STIX]{x1D6E5}}f(x)$$=f(x)$ almost everywhere with respect to Lebesgue meas...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2018-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509418000117/type/journal_article |
| Summary: | We obtain partial improvement toward the pointwise convergence problem of Schrödinger solutions, in the general setting of fractal measure. In particular, we show that, for $n\geqslant 3$, $\lim _{t\rightarrow 0}e^{it\unicode[STIX]{x1D6E5}}f(x)$$=f(x)$ almost everywhere with respect to Lebesgue measure for all $f\in H^{s}(\mathbb{R}^{n})$ provided that $s>(n+1)/2(n+2)$. The proof uses linear refined Strichartz estimates. We also prove a multilinear refined Strichartz using decoupling and multilinear Kakeya. |
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| ISSN: | 2050-5094 |