  We consider the renormalization of the one-loop effective action for the
Yukawa interaction. We compute the beta functions in the generalized
DeWitt-Schwinger subtraction scheme. For the quantized scalar field we obtain
that all the beta functions exhibit decoupling for heavy fields as stated by
the Appelquist-Carazzone theorem including also the gravitational couplings.
For the quantized Dirac field, decoupling appears for almost all of them. We
obtain the atypical result that the mass parameter of the background scalar
field does not decouple.
