Let h d = f = (f k) ∈ ω : k d k | f k − f k+1 | < ∞ ∩ c 0 , where d = (d k) is an unbounded and monotonic increasing sequence of positive reals. We study the matrix domains h d (C q) = (h d) C q and bv(C q) = (bv) C q , where C q is the q-Cesàro matrix, 0 < q < 1. Apart from the inclusion relations and Schauder basis, we compute α-, β-and γ-duals of the spaces h d (C q) and bv(C q). We state and prove theorems concerning characterization of matrix classes from the spaces h d (C q) and bv(C q) to any one of the space ℓ ∞ , c, c 0 or ℓ 1. Finally, we obtain certain identities concerning characterization of compact operators using Hausdorff measure of non-compactness in the space h d (C q).