Abstract
For 1 ≤ p < n , the embeddings of Sobolev spaces WΔ1,p(ΩTn) of functions defined on an open subset of an arbitrary time scale Tn , n ≥ 1 , endowed with the Lebesgue Δ-measure have been developed in (Agarwal et al. in Adv. Differ. Equ. 2006:38121, 2006) for n = 1 and later generalized to arbitrary n ≥ 1 in (Su et al. in Dyn. Partial Differ. Equ. 12(3):241-263, 2015). In this article we present the embeddings of Sobolev spaces WΔ1,p(ΩTn) for n ≤ p ≤ ∞ and then, using these embeddings, we develop general Sobolev's embedding for the Sobolev spaces WΔ1,p(ΩTn) on time scales, where k is a non-negative integer and 1 ≤ p ≤ ∞ .