  We report on a Kondo correlated quantum dot connected to two-dimensional
leads where we demonstrate the renormalization of the g-factor in the pure
Zeeman case i.e, for magnetic fields parallel to the plane of the quantum dot.
For the same system we study the influence of orbital effects by investigating
the quantum Hall regime i.e. a perpendicular magnetic field is applied. In this
case an unusual behaviour of the suppression of the Kondo effect and of the
split zero-bias anomaly is observed. The splitting decreases with magnetic
field and shows discontinuous changes which are attributed to the intricate
interplay between Kondo screening and the quantum Hall edge structure
originating from electrostatic screening. This edge structure made up of
compressible and incompressible stripes strongly affects the Kondo temperature
of the quantum dot and thereby influences the renormalized g-factor.
