Maximal function estimates of solutions to general dispersive partial differential equations
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- by Hans P. Heinig and Sichun Wang PDF
- Trans. Amer. Math. Soc. 351 (1999), 79-108 Request permission
Abstract:
Let $u(x,t)=(S_\Omega f)(x,t)$ be the solution of the general dispersive initial value problem: \[ \partial _tu-i\Omega (D)u=0, \quad u(x,0)=f(x), \qquad (x,t)\in \mathbb {R}^n \times \mathbb {R}\] and $S^{**}_\Omega f$ the global maximal operator of $S_\Omega f$. Sharp weighted $L^p$-esimates for $S^{**}_\Omega f$ with $f\in H_s(\mathbb {R}^n)$ are given for general phase functions $\Omega$.References
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Additional Information
- Hans P. Heinig
- Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada
- Email: heinig@mcmail.cis.mcmaster.ca
- Sichun Wang
- Affiliation: Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada
- Email: wangs@icarus.math.mcmaster.ca
- Received by editor(s): May 5, 1996
- Received by editor(s) in revised form: July 1, 1996
- Additional Notes: The research of the first author was supported in part by NSERC grant A-4837
- © Copyright 1999 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 351 (1999), 79-108
- MSC (1991): Primary 42B25; Secondary 42A45
- DOI: https://doi.org/10.1090/S0002-9947-99-02116-9
- MathSciNet review: 1458324