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The boundedness and the compactness of the two integral operators where g is an analytic function on the open unit disk in the complex plane, on the Zygmund space are studied. where the supremum is taken over all e iθ ∈ ∂D and h > 0. By a Zygmund theorem (see [1, Theorem 5.3]) and the closed graph theorem, we have that f ∈ ᐆ if and only if (1.2) moreover the following asymptotic relation holds:doi:10.1155/2007/32124 fatcat:moqtya3n2vgbpgs6ssolhhkfx4