On the Continuous embeddings between the fractional Hajłasz-Orlicz-Sobolev spaces

Abstract: Let $G$ be an Orlicz function and let $ \alpha, \beta, s$ be positive real numbers. Under certain conditions on the Orlicz function $ G $, we establish some continuous embeddings results between the fractional order Orlicz-Sobolev spaces defined on metric-measure spaces $W_s^{\alpha, G}(X, d, \mu)$ and the fractional Haj{\l}asz-Orlicz-Sobolev spaces $M^{\beta, G}(X,d,\mu)$.