Institution: | a Institute of Mathematics, National Academy of Sciences of Ukraine, Tereschenkivska Street 3, Kyiv 01601, Ukraine b Institut für Mathematik, Universität Würzburg, 97074 Würzburg, Germany |
Abstract: | For the sets , 1?p<∞, of positive finite Borel measures μ on the real axis with the set of algebraic polynomials P dense in Lp(R,dμ), we establish a majorization principle of their “boundaries,” i.e. for every there exists such that dμ/dν?1. A corresponding principle holds for the sets , p>0, of non-negative upper semi-continuous on R functions (weights) w such that P is dense in the space : For every there exists such that w?ω. |