Geodesic
Fourier--Price coefficients of class GM and best approximations of functions in the Lorentz space $L_{p\theta}[0,1)$, $1$, $1\theta+\infty$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximation theory, and related problems of mathematical analysis, Tome 293 (2016), pp. 83-104

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For polynomials in the Price system, we establish an inequality of different metrics in the Lorentz spaces. Applying this inequality, we prove a Hardy–Littlewood theorem for the Fourier–Price series with GM sequences of coefficients in the two-parameter Lorentz spaces and in the Nikol'skii–Besov spaces with a Price basis. We also study the behavior of the best approximations of functions by Price polynomials in the metric of the Lorentz space. 
@article{TM_2016_293_a5,
     author = {A. U. Bimendina and E. S. Smailov},
     title = {Fourier--Price coefficients of class {GM} and best approximations of functions in the {Lorentz} space $L_{p\theta}[0,1)$, $1<p<+\infty$, $1<\theta<+\infty$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {83--104},
     publisher = {mathdoc},
     volume = {293},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2016_293_a5/}
}
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A. U. Bimendina; E. S. Smailov. Fourier--Price coefficients of class GM and best approximations of functions in the Lorentz space $L_{p\theta}[0,1)$, $1