Relations between Schramm spaces and generalized Wiener classes

Abstract

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.

10 pages, To appear in J. Math. Anal. Appl