engleski

One-scale H-distributions

Microlocal defect functionals (H-measures, H- distributions, semiclassical measures etc.) are objects which determine, in some sense, the lack of strong compactness for weakly convergent Lp sequences. In contrast to the semiclassical measures, H-measures are not suitable to treat problems with a characteristic length (e.g. thickness of a plate), while more recant variants, one-scale H-measures, have property of being extension of both H-measures and semiclassical measures. However, H-measures, as well as one-scale- measures, are adequate only for the L2 framework. As the generalisation of H-measures to the Lp - Lp′ setting has already been constructed via H-distributions, here we introduce objects which extends the notion of one-scale H-measures, one-scale H- distributions, as a counterpart of H- distributions with a characteristic length.

H-measures ; H-distributins ; localisation principle ; semiclassical measures ; Fourier multipliers

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