Geodesic
On the Besov and Besov--Nikol'skii Classes and on Estimates for the Mixed Moduli of Smoothness of Fractional Derivatives
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 244-256

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Fractional-order derivatives in the sense of Weyl are considered for functions of several variables. Estimates for the mixed moduli of smoothness for these derivatives are obtained in terms of the mixed moduli of smoothness of the functions themselves. These estimates are applied to study the interrelation between the Besov and Nikol'skii–Besov classes and the other classes of functions. 
@article{TM_2003_243_a17,
     author = {M. K. Potapov and B. V. Simonov and S. Yu. Tikhonov},
     title = {On the {Besov} and {Besov--Nikol'skii} {Classes} and on {Estimates} for the {Mixed} {Moduli} of {Smoothness} of {Fractional} {Derivatives}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {244--256},
     publisher = {mathdoc},
     volume = {243},
     year = {2003},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2003_243_a17/}
}
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M. K. Potapov; B. V. Simonov; S. Yu. Tikhonov. On the Besov and Besov--Nikol'skii Classes and on Estimates for the Mixed Moduli of Smoothness of Fractional Derivatives. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function spaces, approximations, and differential equations, Tome 243 (2003), pp. 244-256. http://geodesic.mathdoc.fr/item/TM_2003_243_a17/