论文标题
多元准投影操作员和傅立叶乘数近似
Approximation by multivariate quasi-projection operators and Fourier multipliers
论文作者
论文摘要
考虑了与函数$φ$和分布/函数$ \widetildeφ$相关的多元准投影运算符$ q_j（f，φ，\widetildeφ）$。函数$φ$应该满足Strang-Fix条件和兼容条件，并具有$ \widetildeφ$。使用基于傅立叶乘数的技术，我们研究了该运算符的近似属性$ f $从各向异性BESOV空间和$ 1 \ le p \ le p \ le \ infty $的$ f $。特别是，从平滑度和最佳近似值方面，$ l_p $ eRROR的上和下部估计值。
Multivariate quasi-projection operators $Q_j(f,φ, \widetildeφ)$, associated with a function $φ$ and a distribution/function $\widetildeφ$, are considered. The function $φ$ is supposed to satisfy the Strang-Fix conditions and a compatibility condition with $\widetildeφ$. Using technique based on the Fourier multipliers, we studied approximation properties of such operators for functions $f$ from anisotropic Besov spaces and $L_p$ spaces with $1\le p\le \infty$. In particular, upper and lower estimates of the $L_p$-error of approximation in terms of moduli of smoothness and best approximations are obtained.
