We continue the study of the fractional variation following the distributional approach developed in the previous works Bruè et al. (2021), Comi and Stefani (2019), Comi and Stefani (2019). We provide a general analysis of the distributional space BVα,p(Rn) of Lp functions, with p∈ [1 , + ∞] , possessing finite fractional variation of order α∈ (0 , 1). Our two main results deal with the absolute continuity property of the fractional variation with respect to the Hausdorff measure and the existence of the precise representative of a BVα,p function.
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