Geodesic
Kolyada inequality between mixed smoothness moduli of functions in the metrics of $L_p$ and $L_\infty$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2022), pp. 3-15

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Interrelations between mixed fractional moduli of smoothness considered in the $L_p$ and $L_\infty$ metrics are clarified in the paper. 
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     author = {M. K. Potapov and B. V. Simonov},
     title = {Kolyada inequality between mixed smoothness moduli of functions in the metrics of $L_p$ and $L_\infty$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {3--15},
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     year = {2022},
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     url = {http://geodesic.mathdoc.fr/item/VMUMM_2022_4_a0/}
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M. K. Potapov; B. V. Simonov. Kolyada inequality between mixed smoothness moduli of functions in the metrics of $L_p$ and $L_\infty$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2022), pp. 3-15. http://geodesic.mathdoc.fr/item/VMUMM_2022_4_a0/