Pointwise differentiability of higher-order for distributions

نویسندگان

چکیده

For distributions, we build a theory of higher order pointwise differentiability comprising, for zero, {\L}ojasiewicz's notion point value. Results include Borel regularity differentials, rectifiability the associated jets, Rademacher-Stepanov type theorem, and Lusin approximation. A substantial part this development is new also zeroth order. Moreover, establish Poincar\'e inequality involving natural norms negative differentiability. As corollary, characterise in terms values distributional partial derivatives.

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ژورنال

عنوان ژورنال: Analysis & PDE

سال: 2021

ISSN: ['2157-5045', '1948-206X']

DOI: https://doi.org/10.2140/apde.2021.14.323