# Relations between Schramm spaces and generalized Wiener classes

## TL;DR

This paper establishes conditions for embeddings between Schramm spaces and generalized Wiener classes, extending several existing results including a key theorem by Perlman and Waterman.

## Contribution

It provides necessary and sufficient criteria for embeddings between specific function spaces, generalizing and unifying previous results in the literature.

## Key findings

- Derived new embedding conditions for Schramm and Wiener spaces.
- Extended fundamental theorems in the theory of function spaces.
- Unified various existing results under a common framework.

## 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.