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Inhomogeneous Strichartz estimatesin some critical cases


Authors: Neal Bez, Jayson Cunanan and Sanghyuk Lee
Journal: Proc. Amer. Math. Soc. 148 (2020), 639-652
MSC (2010): Primary 35J10, 35L05
DOI: https://doi.org/10.1090/proc/14874
Published electronically: November 19, 2019
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Abstract: Strong-type inhomogeneous Strichartz estimates are shown to be false for the wave equation outside the so-called acceptable region. On a critical line where the acceptability condition marginally fails, we prove substitute estimates with a weak-type norm in the temporal variable. We achieve this by establishing such weak-type inhomogeneous Strichartz estimates in an abstract setting. The application to the wave equation rests on a slightly stronger form of the standard dispersive estimate in terms of certain Besov spaces.


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Additional Information

Neal Bez
Affiliation: Department of Mathematics, Graduate School of Science and Engineering, Saitama University, Saitama 338-8570, Japan
Email: nealbez@mail.saitama-u.ac.jp

Jayson Cunanan
Affiliation: Department of Mathematics, Graduate School of Science and Engineering, Saitama University, Saitama 338-8570, Japan
Email: jcunanan@mail.saitama-u.ac.jp

Sanghyuk Lee
Affiliation: Department of Mathematical Sciences and RIM, Seoul National University, Seoul 151-747, Republic of Korea
Email: shklee@snu.ac.kr

DOI: https://doi.org/10.1090/proc/14874
Received by editor(s): April 7, 2019
Published electronically: November 19, 2019
Additional Notes: The first author was supported by JSPS Grant-in-Aid for Young Scientists A No. 16H05995
The second author was supported by JSPS Postdoctoral Research Fellowship No. 18F18020
The third author was supported by NRF-2015R1A4A1041675
Communicated by: Ariel Barton
Article copyright: © Copyright 2019 American Mathematical Society