<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg"><mml:mi>O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msubsup><mml:mrow><mml:mi>?</mml:mi></mml:mrow><mml:mrow><mml:mi>s</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msubsup></mml:math>) polarized heavy flavor corrections to deep-inelastic scattering at Q2 ? m2

We calculate the quarkonic O(?s2) massive operator matrix elements ?AQg(N),?AQqPS(N) and ?Aqq,QNS(N) for twist–2 operators associated heavy flavor Wilson coefficients in polarized deeply inelastic scattering region Q2?m2 to O(?) case of inclusive contributions. The evaluation is performed Mellin space, without applying integration-by-parts method. result given terms harmonic sums. This leads a significant compactification derived previously [1], which we partly confirm, also correct. results allow determine g1(x,Q2) all but power suppressed ?(m2/Q2)k,k?1. momentum fraction z-space are presented. discuss small x effects case. Numerical compute gluonic matching two–mass variable number scheme O(?).