Geodesic
On Best Approximations by Analogs of ``Proper'' and ``Improper'' Hyperbolic Crosses
Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 466-476

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The exact approximation orders for the classes $H_q^\Omega$ are calculated for the case in which $\Omega(t)$ contains both power and logarithmic multipliers. For these classes, the exact orders of best approximation by analogs of “improper” hyperbolic crosses are also obtained.
Keywords: best approximation orders for the classes $H_q^\Omega$, hyperbolic cross, orthowidth, trigonometric polynomial, Nikolskii function class. 
@article{MZM_2013_93_3_a14,
     author = {N. N. Pustovoitov},
     title = {On {Best} {Approximations} by {Analogs} of {``Proper''} and {``Improper''} {Hyperbolic} {Crosses}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {466--476},
     publisher = {mathdoc},
     volume = {93},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a14/}
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N. N. Pustovoitov. On Best Approximations by Analogs of ``Proper'' and ``Improper'' Hyperbolic Crosses. Matematičeskie zametki, Tome 93 (2013) no. 3, pp. 466-476. http://geodesic.mathdoc.fr/item/MZM_2013_93_3_a14/