Geodesic
An embedding theorem for functions of class $\operatorname{Lip}1$
Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 357-366

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We prove a theorem giving necessary and sufficient conditions for embedding the class $\operatorname{Lip}1$ in a class of functions which is defined in terms of the absolute convergence of series of Fourier coefficients with respect to the Faber-Schauder system, normalized in $L_2$. 
@article{MZM_1975_18_3_a4,
     author = {T. N. Saburova},
     title = {An embedding theorem for functions of class $\operatorname{Lip}1$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {357--366},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a4/}
}
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T. N. Saburova. An embedding theorem for functions of class $\operatorname{Lip}1$. Matematičeskie zametki, Tome 18 (1975) no. 3, pp. 357-366. http://geodesic.mathdoc.fr/item/MZM_1975_18_3_a4/