Non Existence of Principal Values of Signed Riesz Transforms of Non Integer Dimension
نویسندگان
چکیده
In this paper we prove that, given s ≥ 0, and a Borel non zero measure μ in Rm, if for μ-almost every x ∈ Rm the limit lim ε→0 ∫ |x−y|>ε x −y |x −y|s+1 dμ(y) exists and 0 < lim supr→0 μ(B(x, r))/r s < ∞, then s in an integer. In particular, if E ⊂ Rm is a set with positive and bounded s-dimensional Hausdorff measure Hs and for Hs-almost every x ∈ E the limit
منابع مشابه
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