Imbedding theorems for Lipschitz spaces generated by the weak-\(L^p\) metric (Q1270272)

Given a normed space \(X\) of functions, one may define a modulus of smoothness with respect to \(X\) and consider a space \(\Lambda_X^\alpha(R^n)\) where this modulus satisfies certain growth conditions. Various imbedding theorems for such spaces are proved when \(X=L^{p,\infty}\) is a weak-\(L^p\) space. Since \(L^{p,\infty}\subseteq L^p\), some of these theorems generalize results from [\textit{R. A. DeVore} and \textit{G. G. Lorentz} [``Constructive approximation'' (1993; Zbl 0797.41016)]. The proofs are based on measure theoretic arguments, not on Fourier transforms. This allows to consider also \(p<1\).