Inhomogeneous Strichartz estimatesin some critical cases

Bez, Neal; Cunanan, Jayson; Lee, Sanghyuk

doi:10.1090/proc/14874

Inhomogeneous Strichartz estimatesin some critical cases
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by Neal Bez, Jayson Cunanan and Sanghyuk Lee PDF

Proc. Amer. Math. Soc. 148 (2020), 639-652 Request permission

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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