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~In this paper, we investigate the boundedness of some Volterra-typeoperators between ~$Zygmund$~ type spaces. Then, we give the essential norms ofsuch operators in terms of ~$g,\varphi$, their derivatives and the n-th power~$\varphi^n$ of ~$\varphi$.

Essential norms of Volterra-type operators between~$Zygmund$~ type spaces