Sobolev’s embedding on time scales

For [Formula: see text] , the embeddings of Sobolev spaces [Formula: see text] of functions defined on an open subset of an arbitrary time scale [Formula: see text] , [Formula: see text] , endowed with the Lebesgue Δ-measure have been developed in (Agarwal et al. in Adv. Differ. Equ. 2006:38121, 2006) for [Formula: see text] and later generalized to arbitrary [Formula: see text] in (Su et al. in Dyn. Partial Differ. Equ. 12(3):241–263, 2015). In this article we present the embeddings of Sobolev spaces [Formula: see text] for [Formula: see text] and then, using these embeddings, we develop general Sobolev’s embedding for the Sobolev spaces [Formula: see text] on time scales, where k is a non-negative integer and [Formula: see text] .