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A global space-time estimate for dispersive operators through its local estimate
- Author(s)
- Cho, Chu-Hee, Koh, Youngwoo, Lee, Jungjin
- Issued Date
- 2022-10
- Citation
- JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.514, no.1, pp.126255
- Abstract
- We will show that a local space-time estimate implies a global space-time estimate for dispersive operators. In order for this implication we consider a Littlewood-Paley type square function estimate for dispersive operators in a time variable and a generalization of Tao's epsilon removal lemma in mixed norms. By applying this implication to the fractional Schrodinger equation in R2+1 we obtain the sharp global space-time estimates with optimal regularity from the previous known local ones. (C) 2022 Elsevier Inc. All rights reserved.
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- ISSN
- 0022-247X
- Keyword (Author)
- Schrodinger equation, Dispersive operator, Global space-time estimate
- Keyword
- WELL-POSEDNESS, WAVE
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