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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We are interested in the computability of the invariant measures in a computable dynamical system. We construct two counter-examples. The first one has a unique SRB measure, which is not computable. The second one has no computable invariant measure at all. The systems are topological, i.e. continuous transformations on compact spaces, so they admit invariant measures. A topological dynamical s...
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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.
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We construct quasiconformal mappings in Euclidean spaces by integration of a discontinuous kernel against doubling measures with suitable decay. The differentials of mappings that arise in this way satisfy an isotropic form of the doubling condition. We prove that this isotropic doubling condition is satisfied by the distance functions of certain fractal sets. Finally, we construct an isotropic...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.12.014