Perturbed Sobolev spaces H^{s,p}_α admit an analogue description in terms of standard Sobolev spaces, extending Strichartz estimates and yielding local well-posedness for the singularly perturbed NLS in 2D and 3D.
Geometric theory of semilinear parabolic equations , volume 840 of Lecture Notes in Mathe- matics
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Fractional Sobolev Spaces for the Singular-perturbed Laplace Operator in the $L^p$ setting
Perturbed Sobolev spaces H^{s,p}_α admit an analogue description in terms of standard Sobolev spaces, extending Strichartz estimates and yielding local well-posedness for the singularly perturbed NLS in 2D and 3D.