Pointwise Convergence of the Fractional Schrödinger Equation in ℝ
We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in ℝ². By establishing Hs (ℝ²) L³(ℝ²) estimates for the associated maximal operator provided that s > 1/3, we improve the previous result obtained by Miao, Yang, and Zheng [19]. Our estimates extend th...
Gespeichert in:
| Veröffentlicht in: | Taiwanese journal of mathematics 2022-02, Vol.26 (1), p.177-200 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in ℝ². By establishing Hs
(ℝ²) L³(ℝ²) estimates for the associated maximal operator provided that s > 1/3, we improve the previous result obtained by Miao, Yang, and Zheng [19]. Our estimates extend the refined Strichartz estimates obtained by Du, Guth, and Li [10] to a general class of elliptic functions. |
|---|---|
| ISSN: | 1027-5487 2224-6851 |
| DOI: | 10.11650/tjm/210904 |