Abstract: This is the second talk in the series devoted to the local and nonlocal geometry of Besov, Lebesgue,Lizorkin-Triebel, Sobolev and sequence spaces.

One considers the Hausdorff, Kuratovski,
and separation measures of noncompactness, the corresponding moduli and the constants D and W on on various spaces, including the anisotropic spaces of differentiable functions defined on an open subset of the Euclidean space, and calculates or evaluates the constants.

One of the tools is the strengthened
version of the estimates related to the weak continuity of the generalised duality mapping.

The questions of sharpness, open problems and applications to Nonlinear Analysis and PDE
are discussed.