Displaying similar documents to “Problems on distortion under conformal mapping.”

On a theorem of Haimo regarding concave mappings

Martin Chuaqui, Peter Duren, Brad Osgood (2011)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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A relatively simple proof is given for Haimo’s theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo’s criterion, which is now shown to be sharp. It is proved that Haimo’s functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presence of corners.

On a theorem of Haimo regarding concave mappings

Martin Chuaqui, Peter Duren, Brad Osgood (2011)

Annales UMCS, Mathematica

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A relatively simple proof is given for Haimo's theorem that a meromorphic function with suitably controlled Schwarzian derivative is a concave mapping. More easily verified conditions are found to imply Haimo's criterion, which is now shown to be sharp. It is proved that Haimo's functions map the unit disk onto the outside of an asymptotically conformal Jordan curve, thus ruling out the presence of corners.

Boundedness of sublinear operators on the homogeneous Herz spaces.

Guoen Hu (2003)

Publicacions Matemàtiques

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Some boundedness results are established for sublinear operators on the homogeneous Herz spaces. As applications, some new theorems about the boundedness on homogeneous Herz spaces for commutators of singular integral operators are obtained.