Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator

Geometric Characterizations of the Differential Shift Plus Alexander Integral Operator

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In this toys effort, we deal with a new integral operator in the open unit disk.This operator is formulated by the complex Alexander operator and its derivative.Furthermore, we introduce a new subspace of the Hardy space containing the normalized analytic functions.

We shall prove that the new integral operator is closed in the subspace of normalized functions.Geometric characterizations Puzzle are established in the sequel based on the maximality of Jack Lemma.