  We give necessary and sufficient conditions for the embeddings
$\Lambda\text{BV}^{(p)}\subseteq \Gamma\text{BV}^{(q_n\uparrow q)}$ and
$\Phi\text{BV}\subseteq\text{BV}^{(q_n\uparrow q)}$. As a consequence, a number
of results in the literature, including a fundamental theorem of Perlman and
Waterman, are simultaneously extended.
