Analytic inversion of adjunction: L^2 extension theorems with gain
  We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions that we call denominators. We give a collection of examples of these denominators related to the divisor defined by the submanifold. 
Jeffery D. McNeal, Dror Varolin