Fourier transform and regularity of characteristic functions
Open Access
- 21 November 2016
- journal article
- Published by American Mathematical Society (AMS) in Proceedings of the American Mathematical Society
- Vol. 145 (3) , 1097-1107
Abstract
Let E E be a bounded domain in R d \mathbb R^d . We study regularity property of χ E \chi _E and integrability of χ E ^ \widehat {\chi _E } when its boundary ∂ E \partial E satisfies some conditions. At the critical case these properties are generally known to fail. By making use of Lorentz and Lorentz-Sobolev spaces we obtain the endpoint cases of the previous known results. Our results are based on a refined version of Littlewood-Paley inequality, which makes it possible to exploit cancellation effectively.Keywords
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Funding Information
- National Research Foundation of Korea
- National Research Foundation of Korea
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