ON THE PROBLEM OF SHARP EXPONENTS IN MULTIVARIATE NIKOLSKII-TYPE INEQUALITIES

[摘要] Let OMEGA subset-of R(N) be a bounded open set, w a weight-function, p > 0, and alpha > 0. Assuming some regularity conditions on w and the boundary partial derivativeOMEGA of OMEGA we prove that if grad w not-equal 0 on the set GAMMA where w vanishes and if GAMMA is transversal to partial derivativeOMEGA then there exists a positive constant C such that for any polynomial P of degree at most n we have \\P\\p,OMEGA less-than-or-equal-to Cn(alpha) \\P\w\2\\p, OMEGA; furthermore the exponent alpha of n is optimal. (C) 1994 Academic Press, Inc.

[发布日期] 1994-05-01