This paper is a direct followup of the recent author's paper. In this paper we continue to analyze approximation and recovery properties with respect to systems satisfying universal sampling discretization property and a special unconditionality property. In addition we assume that the subspace spanned by our system satisfies some Nikol'skii-type inequalities. We concentrate on recovery with the error measured in the $L_p$ norm for $2\le p<\infty$. We apply a powerful nonlinear approximation method -- the Weak Orthogonal Matching Pursuit (WOMP) also known under the name Weak Orthogonal Greedy Algorithm (WOGA). We establish that the WOMP based on good points for the $L_2$-universal discretization provides good recovery in the $L_p$ norm for $2\le p<\infty$. For our recovery algorithms we obtain both the Lebesgue-type inequalities for individual functions and the error bounds for special classes of multivariate functions. We combine here two deep and powerful techniques -- Lebesgue-type inequalities for the WOMP and theory of the universal sampling dicretization -- in order to obtain new results in sampling recovery.

翻译：本文是作者近期论文的直接后续研究。本文继续分析在满足通用采样离散化性质和特殊无条件下，相对于某些系统的逼近与恢复性质。此外，我们假设由该系张成的子空间满足某种Nikol'skii型不等式。我们重点研究在$L_p$范数（$2\le p<\infty$）下误差测量的恢复问题。我们采用一种强大的非线性逼近方法——弱正交匹配追踪（WOMP），也称为弱正交贪婪算法（WOGA）。我们证明，基于$L_2$通用离散化优点的WOMP方法，在$2\le p<\infty$的$L_p$范数下具有良好的恢复性能。对于所提出的恢复算法，我们既获得了针对单个函数的Lebesgue型不等式，也获得了针对多变量函数特殊类的误差界。通过结合两种深刻而强大的技术——WOMP的Lebesgue型不等式与通用采样离散化理论——我们得到了采样恢复领域的新结果。