THE POINCARé INEQUALITY AND LOGARITHMIC SOBOLEV INEQUALITY FOR A SPHERICALLY CENSORED GAUSSIAN MEASURE

摘要

For a one-dimensional projection of a spherically censored Gaussian measure on R~n, the logarithmic Sobolev inequality is proved. As a consequence, we obtain the Poincaré inequality for a spherically censored Gaussian measure on R~n, n ≥ 3.