Geodesic
Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying H\"older Conditions
Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 26-34

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We prove a new sharp Kolmogorov-type inequality that estimates the uniform norm of a mixed derivative of fractional order (in the sense of Marchaud) of a function of several variables via the uniform norm of the function and its norm on Hölder spaces.
Keywords: Marchaud fractional derivative, essentially bounded function, Kolmogorov-type inequality, Hölder condition, Hölder space. 
@article{MZM_2010_87_1_a3,
     author = {V. F. Babenko and S. A. Pichugov},
     title = {Sharp {Estimates} of the {Norms} of {Fractional} {Derivatives} of {Functions} of {Several} {Variables} {Satisfying} {H\"older} {Conditions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {26--34},
     publisher = {mathdoc},
     volume = {87},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a3/}
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V. F. Babenko; S. A. Pichugov. Sharp Estimates of the Norms of Fractional Derivatives of Functions of Several Variables Satisfying H\"older Conditions. Matematičeskie zametki, Tome 87 (2010) no. 1, pp. 26-34. http://geodesic.mathdoc.fr/item/MZM_2010_87_1_a3/