Geodesic
A Littlewood--Paley type theorem and a~corollary
Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1155-1194.

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We prove an analogue of the Littlewood–Paley theorem for orthoprojectors onto mutually orthogonal subspaces of piecewise-polynomial functions on the cube $I^d$. This yields upper bounds for the norms of functions in $L_p(I^d)$ in terms of the corresponding norms of the projections to subspaces of piecewise-polynomial functions of several variables. We use these results to obtain upper bounds for the Kolmogorov widths of Besov classes of (non-periodic) functions satisfying mixed Hölder conditions.
Keywords: orthoprojector, mutually orthogonal subspaces, piecewise-polynomial functions, Littlewood–Paley theorem, width. 
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S. N. Kudryavtsev. A Littlewood--Paley type theorem and a~corollary. Izvestiya. Mathematics , Tome 77 (2013) no. 6, pp. 1155-1194. http://geodesic.mathdoc.fr/item/IM2_2013_77_6_a3/

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