On embeddings between spaces of functions of generalized bounded variation

In this note, we aim to establish a number of embeddings between various function spaces that are frequently considered in the theory of Fourier series. More specifically, we give sufficient conditions for the embeddings $\Phi V[h]\subseteq \Lambda$\text{BV}$^{(p_n\uparrow p)}$,$\Lambda V[h_1]^{(p)}\subseteq\Gamma V[h_2]^{(q)}$and$\Lambda$\text{BV}$^{(p_n\uparrow p)}\subseteq\Gamma$\text{BV}$^{(q_n\uparrow q)}$. Our results are new even for the well-known spaces that have been studied in the literature. In particular, a number of results due to M. Avdispahi'{c}, that describe relationships between the classes $\mathrm{\Lambda }\text{BV}$ and $V[h]$, are derived as special cases.