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Integral transforms of functions with restricted derivatives

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Brown J.

Annales Polonici Mathematici

2007

tom 91

nr 1

85-97

We show that functions whose derivatives lie in a half-plane are preserved under the Pommerenke, Chandra-Singh, Libera, Alexander and Bernardi integral transforms. We determine precisely how these transforms act on such functions. We prove that if the derivative of a function lies in a convex region then the derivative of its Pommerenke, Chandra-Singh, Libera, Alexander and Bernardi transforms lie in a strictly smaller convex region which can be determined. We also consider iterates of these transforms. Best possible results are obtained.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Brown J.

1 2007

Wyniki wyszukiwania

Integral transforms of functions with restricted derivatives