  We analyze the Weyl invariance constraints on higher spin vertex operators in
open superstring theory describing massless higher spin gauge field excitations
in d-dimensional space-time. We show that these constraints lead to low-energy
equations of motion for higher spin fields in AdS space, with the leading order
beta-function for the higher spin fields producing Fronsdal's operator in
$AdS_{d+1}$, despite that the higher spin vertex operators are originally
defined in flat background. The correspondence between the $\beta$-function in
string theory and $AdS_{d+1}$ Fronsdal operators in space-time is found to be
exact for $d=4$, while for other space-time dimensions it requires
modifications of manifest expressions for the higher spin vertex operators.
  We argue that the correspondence considered in this paper is the leading
order of more general isomorphism between Vasiliev's equations and equations of
motion of extended open string field theory (OSFT), generalized to include the
higher spin operators.
