Regularity for the CR vector bundle problem II
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 1, pp. 129-191.

We derive a 𝒞 k+1 2 Hölder estimate for Pϕ, where P is either of the two solution operators in Henkin’s local homotopy formula for ¯ b on a strongly pseudoconvex real hypersurface M in n , ϕ is a (0,q)-form of class 𝒞 k on M, and k0 is an integer. We also derive a 𝒞 a estimate for Pϕ, when ϕ is of class 𝒞 a and a0 is a real number. These estimates require that M be of class 𝒞 k+5 2 , or 𝒞 a+2 , respectively. The explicit bounds for the constants occurring in these estimates also considerably improve previously known such results.

These estimates are then applied to the integrability problem for CR vector bundles to gain improved regularity. They also constitute a major ingredient in a forthcoming work of the authors on the local CR embedding problem.

Publié le :
Classification : 32V05, 32A26, 32T15
Gong, Xianghong 1 ; Webster, Sidney M. 2

1 Department of Mathematics University of Wisconsin Madison, WI 53706, USA
2 Department of Mathematics University of Chicago Chicago, IL 60637, USA
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Gong, Xianghong; Webster, Sidney M. Regularity for the CR vector bundle problem II. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 10 (2011) no. 1, pp. 129-191. http://www.numdam.org/item/ASNSP_2011_5_10_1_129_0/

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