  We derive a number of exact relations between response functions of
holomorphic, chiral fractional quantum Hall states and their particle-hole (PH)
conjugates. These exact relations allow one to calculate the Hall conductivity,
Hall viscosity, various Berry phases, and the static structure factor of
PH-conjugate states from the corresponding properties of the original states.
These relations establish a precise duality between chiral quantum Hall states
and their PH-conjugates. The key ingredient in the proof of the relations is a
generalization of Girvin's construction of PH-conjugate states to inhomogeneous
magnetic field and curvature. Finally, we make several non-trivial checks of
the relations, including for the Jain states and their PH-conjugates.
