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In this paper a Banach function space (b.f.s. in short)on a  n -dimensional bounded domain Ω with Lebesgue measure is considered. The Banach function spaceon the-dimensional surfacegenerated by the norm of the spaceis defined. The Sobolev function spaceis defined using the norm of the spaceas well as the concept of the trace of an arbitrary function from this space on the surface  S . Based on this concept, the space of tracesis defined and a characterization of this space is given. It was proved that it is boundedly embedded in the spaceParticular cases of a functional spacecan be Lebesgue spaces, Lebesgue spaces with variable summability exponents, Morrey space, Orlicz space, grand Lebesgue spaces and etc. The obtained results allow us to consider boundary value problems for differential equations in b.f.s.

The Concept of a Trace and the Boundedness of the Trace Operator in Banach-Sobolev Function Spaces