We prove the optimality of the hypotheses guaranteeing the Lp-boundedness for the Cauchy-Leray integral in Cn, n ≥ 2, obtained in [LS-4]. Two domains, both elementary in nature, show that the geometric requirement of strong C-linear convexity, and the regularity of order 2, are both necessary.
Lanzani, L., Stein, E.M. (2019). The cauchy-leray integral: Counterexamples to the Lp-theory. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 68(5), 1609-1621 [10.1512/iumj.2019.68.7786].
The cauchy-leray integral: Counterexamples to the Lp-theory
Lanzani L.
;
2019
Abstract
We prove the optimality of the hypotheses guaranteeing the Lp-boundedness for the Cauchy-Leray integral in Cn, n ≥ 2, obtained in [LS-4]. Two domains, both elementary in nature, show that the geometric requirement of strong C-linear convexity, and the regularity of order 2, are both necessary.File in questo prodotto:
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