Sobolev estimates for averaging operators over a convex hypersurface in R3

Abstract

We prove sharp L p -Sobolev estimates for averaging operators associated with a certain type of convex hypersurface in R 3 .

Corrigendum to “Sobolev estimates for averaging operators over a convex hypersurface in R3” [J. Math. Anal. Appl. 412 (1) (2014) 244–268]

“…To prove Proposition 1.1 in [3], we used Lemma 6.2 together with van der Corput lemma. But we have found that there are technical errors in (6, 9) and (6, 10) of Proposition 1.1.…”

“…But we have found that there are technical errors in (6, 9) and (6, 10) of Proposition 1.1. To correct these errors, we replace Lemma 6.2 in [3] by Lemma 1.1. Let a, b and M be positive even integers satisfying a 2 + b M ≥ 1, and let Φ be a function of the form…”