POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES
Forum of Mathematics, Sigma, Tome 6 (2018)
Voir la notice de l'article provenant de la source Cambridge University Press
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.
@article{10_1017_fms_2018_11,
author = {XIUMIN DU and LARRY GUTH and XIAOCHUN LI and RUIXIANG ZHANG},
title = {POINTWISE {CONVERGENCE} {OF} {SCHR\"ODINGER} {SOLUTIONS} {AND} {MULTILINEAR} {REFINED} {STRICHARTZ} {ESTIMATES}},
journal = {Forum of Mathematics, Sigma},
publisher = {mathdoc},
volume = {6},
year = {2018},
doi = {10.1017/fms.2018.11},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.11/}
}
TY - JOUR AU - XIUMIN DU AU - LARRY GUTH AU - XIAOCHUN LI AU - RUIXIANG ZHANG TI - POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES JO - Forum of Mathematics, Sigma PY - 2018 VL - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.11/ DO - 10.1017/fms.2018.11 LA - en ID - 10_1017_fms_2018_11 ER -
%0 Journal Article %A XIUMIN DU %A LARRY GUTH %A XIAOCHUN LI %A RUIXIANG ZHANG %T POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES %J Forum of Mathematics, Sigma %D 2018 %V 6 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.1017/fms.2018.11/ %R 10.1017/fms.2018.11 %G en %F 10_1017_fms_2018_11
XIUMIN DU; LARRY GUTH; XIAOCHUN LI; RUIXIANG ZHANG. POINTWISE CONVERGENCE OF SCHRÖDINGER SOLUTIONS AND MULTILINEAR REFINED STRICHARTZ ESTIMATES. Forum of Mathematics, Sigma, Tome 6 (2018). doi: 10.1017/fms.2018.11
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