Integral transforms of functions with restricted derivatives

Johnny E. Brown. "Integral transforms of functions with restricted derivatives." Annales Polonici Mathematici 91.1 (2007): 85-97. <http://eudml.org/doc/280942>.

@article{JohnnyE2007,
abstract = {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.},
author = {Johnny E. Brown},
journal = {Annales Polonici Mathematici},
keywords = {integral transforms},
language = {eng},
number = {1},
pages = {85-97},
title = {Integral transforms of functions with restricted derivatives},
url = {http://eudml.org/doc/280942},
volume = {91},
year = {2007},
}

TY - JOUR
AU - Johnny E. Brown
TI - Integral transforms of functions with restricted derivatives
JO - Annales Polonici Mathematici
PY - 2007
VL - 91
IS - 1
SP - 85
EP - 97
AB - 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.
LA - eng
KW - integral transforms
UR - http://eudml.org/doc/280942
ER -