Abstract
We describe a class of potentials v = G ∗ f , such that if x0 is from extended singular set of v , that is, r−N ∫ Br(x0) v(x) dx → +∞ for some sequence r → 0 , then necessarily v(x0) = ∞ . This class includes Bessel potentials and Riesz potentials. The result was exploited in our previous paper in order to show that singular dimension of the Bessel potential space Lα,p(RN) (that is, the supremum of Hausdorff’s dimension of extended singular sets, taken over all functions from the space) is equal to N − αp , provided αp N . Mathematics subject classification (2000): 26A12, 31C40, 46E35.
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