BOUNDARY REGULARITY OF BERGMAN KERNEL IN HoLDER SPACE

Let D be a bounded strictly pseudoconvex domain in Cn. Assuming bD & ISIN; Ck+3+& alpha; where k is a nonnegative integer and 0 < & alpha; < 1, we show that (1) the Bergman kernel B( & BULL; , w0) & ISIN; Ck+min{& alpha;,1/2}( over bar D), for any w0 & ISIN; D and (2) the Bergman projection on D is a bounded operator from Ck+& beta; (D) to Ck+min{& alpha;,& beta; /2}(D) for any 0 < & beta; < 1. Our results both improve and generalize the work of E. Ligocka.