Geodesic
Strengthened Ul'yanov's inequality for complete moduli of smoothness of functions from spaces with mixed metrics
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2018), pp. 8-20

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For functions of one variable Ul'yanov inequality about the connection between modulus of continuity in different metrics is well known. In this paper functions of two variables are analyzed. Sharp Ul'yanov inequality for function's full modulus of smoothness of positive order in the different mixed metrics is proved. 
@article{VMUMM_2018_6_a1,
     author = {M. K. Potapov and B. V. Simonov},
     title = {Strengthened {Ul'yanov's} inequality for complete moduli of smoothness of functions from spaces with mixed metrics},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {8--20},
     publisher = {mathdoc},
     number = {6},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_6_a1/}
}
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M. K. Potapov; B. V. Simonov. Strengthened Ul'yanov's inequality for complete moduli of smoothness of functions from spaces with mixed metrics. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2018), pp. 8-20. http://geodesic.mathdoc.fr/item/VMUMM_2018_6_a1/