  One of the important technical tools in Gaitsgory's proof of the Vanishing
Conjecture appearing in the geometric Langlands correspondence ([3]) is the
theory of Whittaker functors for GL_n. We define Whittaker functors for GSp_4
and study their properties. In a sense, these functors correspond to the
maximal parabolic subgroup of GSp_4, whose unipotent radical is not
commutative.
  We also study similar functors corresponding to the Siegel parabolic subgroup
of GSp_4, they are related with Bessel models for GSp_4 and Waldspurger models
for GL_2.
  We define the Waldspurger category, which is a geometric counterpart of the
Waldspurger module over the Hecke algebra of GL_2. We prove a geometric version
of the multiplicity one result for Waldspurger models.
