ON POINTWISE CONVERGENCE OF SCHRÖDINGER MEANS. Issue 2 (30th March 2020)

• Record Type: Journal Article
• Authors: Dimou, Evangelos; Seeger, Andreas
• Is Part Of: Mathematika. Volume 66:Issue 2(2020)
• Page Start: 356
• Page End: 372
• Publication Date: 2020-03-30
• Subjects: 42B25 (primary) -- 35Q41 (secondary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/mtk.12025
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract: For functions in the Sobolev space H s and decreasing sequences t n → 0 we examine convergence almost everywhere of the generalized Schrödinger means on the real line, given by S a f ( x, t n ) = exp ( i t n ( − ∂ x x ) a / 2 ) f ( x ) ; here a > 0, a ≠ 1 . For decreasing convex sequences we obtain a simple characterization of convergence a.e. for all functions in H s when 0 < s < min { a / 4, 1 / 4 } and a ≠ 1 . We prove sharp quantitative local and global estimates for the associated maximal functions. We also obtain sharp results for the case a = 1 .