The Poincaré inequality and logarithmic Sobolev inequality for a spherically censored Gaussian measure

For a one-dimensional projection of a spherically censored Gaussian measure on Rn\mathbf {R}^{n}, the logarithmic Sobolev inequality is proved. As a consequence, we obtain the Poincaré inequality for a spherically censored Gaussian measure on Rn\mathbf {R}^{n}, n≥3n \geq 3.