Abstract:
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.
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