naa a22 4500 510811620 CHVBK 20180411083445.0 cr unu---uuuuu 180411e20130401xx s 000 0 eng 10.1134/S0081543813010045 doi (NATIONALLICENCE)springer-10.1134/S0081543813010045 Bourgain J. Institute for Advanced Study, Einstein Drive, 08540, Princeton, NJ, USA aut On the Schrödinger maximal function in higher dimension [Elektronische Daten] [J. Bourgain] New estimates on the maximal function associated to the linear Schrödinger equation are established. It is shown that the almost everywhere convergence property of e itΔ f for t → 0 holds for f ∈ H s (ℝ n ), $$s > \tfrac{1} {2} - \tfrac{1} {{4n}}$$ , which is a new result for n ≥ 3. We also construct examples showing that $$s \geqslant \tfrac{1} {2} - \tfrac{1} {n}$$ is certainly necessary when n ≥ 4. This is a further contribution to our understanding of how L. Carleson's result for n = 1 generalizes in higher dimension. From the methodological point of view, crucial use is made of J. Bourgain and L. Guth's results and techniques that are based on the multi-linear oscillatory integral theory developed by J. Bennett, T. Carbery and T. Tao. Pleiades Publishing, Ltd., 2013 Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 46-60 0081-5438 280:1<46 2013 280 11501 https://doi.org/10.1134/S0081543813010045 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813010045 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Bourgain J. Institute for Advanced Study, Einstein Drive, 08540, Princeton, NJ, USA aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 280/1(2013-04-01), 46-60 0081-5438 280:1<46 2013 280 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer