منابع مشابه
On fractional calculus associated to doubling and non-doubling measures
In this paper we present several proofs on the extension of M. Riesz fractional integration and di¤erentiation to the contexts of spaces of homogeneous type and measure metric spaces with non-doubling measures. 1. Introduction, some de nitions, and a basic lemma Professor M. Ash asked me to write a survey article on some of the results that Stephen Vági and I obtained in the nineties on fractio...
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In this note, we study sets on the real line which are null with respect to all doubling measures on R, or with respect to all dyadic doubling measures on R. We give some suucient conditions for the former, a test for the latter, and some examples. Our work is motivated by a characterization of dyadic doubling measures by Feeerman, Kenig and Pipher 5], and by a result of Martio 8] on porous set...
متن کاملRemarks on the Nonexistence of Doubling Measures
We establish that there are bounded Jordan domains Ω ⊂ R (n ≥ 2) that do not carry a (nontrivial) doubling measure with respect to the Euclidean distance. More generally, it is shown that every nonempty metric space (X, d) without isolated points has an open and dense subset A such that (A, d) does not carry a doubling measure.
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It is known that in low dimensions supports of Hölder doubling measures are C1,β manifolds. In higher dimensions singularities may occur. We provide a full description of such supports by showing that they are C1,β manifolds away from a closed set of measure zero and that at singular points they are uniformly far from being flat at every scale.
متن کاملOn geometric characterizations for Monge–Ampère doubling measures
In this article we prove a theorem on the size of the image of sections of a convex function under its normal mapping when the sections satisfy a geometric property. We apply this result to get new geometric characterizations for Monge–Ampère doubling measures. 2002 Elsevier Science (USA). All rights reserved.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2019
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/14493