On the best n-term approximation for general Wiener-type spaces

In this paper, we investigate the best [Formula: see text]-term approximation problem for general Wiener-type spaces in the [Formula: see text] sense. Previous work estimated the approximation error under the Bernstein discretization condition, which is often nontrivial to verify, and the constants involved typically lacked explicit quantitative estimates. In this paper, we replace this condition with a simpler condition of Hölder continuity and establish an explicit approximation error bound. As a corollary, we fully resolve an open question regarding the sampling recovery of some Wiener-type space.