Spin-dependent structure functions of real and virtual photons

The implications of the positivity constraint, \g(1)(gamma (P2))(x, Q(2))\ less than or equal to F(1)gamma ((P2))(x-Q(2)), on the presently unknown sp in-dependent structure function g(1)(gamma (P2))(x,Q(2)) of real and virtua l photons are studied at scales Q2 much greater than P2 where longitudinall y polarized photons dominate physically relevant cross sections. In particu lar it is shown how to implement the physical constraints of positivity and continuity at P-2 = 0 in NLO calculations which afford a nontrivial choice of suitable (DIS) factorization schemes related to g(1)(gamma) and F-1(gam ma) and appropriate boundary conditions for the polarized parton distributi ons of real and virtual photons. The predictions of two extreme 'maximal' a nd 'minimal- saturation scerlarios are presented and compared with results obtained within the framework of a simple quark 'hox' calculation expected to yield reasonable estimates in the not too small regions of x and P-2.