We derive a Hölder estimate for , where is either of the two solution operators in Henkin’s local homotopy formula for on a strongly pseudoconvex real hypersurface in , is a -form of class on , and is an integer. We also derive a estimate for , when is of class and is a real number. These estimates require that be of class , or , 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.
@article{ASNSP_2011_5_10_1_129_0, author = {Gong, Xianghong and Webster, Sidney M.}, title = {Regularity for the {CR} vector bundle problem {II}}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {129--191}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 10}, number = {1}, year = {2011}, mrnumber = {2829316}, zbl = {1223.32022}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2011_5_10_1_129_0/} }
TY - JOUR AU - Gong, Xianghong AU - Webster, Sidney M. TI - Regularity for the CR vector bundle problem II JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2011 SP - 129 EP - 191 VL - 10 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2011_5_10_1_129_0/ LA - en ID - ASNSP_2011_5_10_1_129_0 ER -
%0 Journal Article %A Gong, Xianghong %A Webster, Sidney M. %T Regularity for the CR vector bundle problem II %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2011 %P 129-191 %V 10 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2011_5_10_1_129_0/ %G en %F ASNSP_2011_5_10_1_129_0
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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