Estimates for $L_p$ Modules of Continuity on Domains with an Irregular Boundary and Embedding Theorems

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.