Geodesic
Estimates for $L_p$ Modules of Continuity on Domains with an Irregular Boundary and Embedding Theorems
Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 21-33

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The aim of this paper is to study differentiable functions of several variables defined on a domain $G\subset\mathbb{R}$ with irregular boundary. We suggest a new integral representation, which allow us to establish estimates for $L_p$-modules of continuity and embedding theorems for functional spaces that have defined $L_p$-modules of continuity behavior. 
@article{CMFD_2007_25_a2,
     author = {O. V. Besov},
     title = {Estimates for $L_p$ {Modules} of {Continuity} on {Domains} with an {Irregular} {Boundary} and {Embedding} {Theorems}},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {21--33},
     publisher = {mathdoc},
     volume = {25},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_25_a2/}
}
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O. V. Besov. Estimates for $L_p$ Modules of Continuity on Domains with an Irregular Boundary and Embedding Theorems. Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 21-33. http://geodesic.mathdoc.fr/item/CMFD_2007_25_a2/