Elementary density bounds for self-similar sets and application |
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| Authors: | Shaoyuan Xu Weiyi Su |
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| Institution: | (1) School of Mathematics and Computer Science, Gannan Teachers College, Ganzhou, 341000, P. R. China;(2) Department of Mathematics, Nanjing University, Nanjing, 210093, P. R China |
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| Abstract: | Falconer1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at HS-almost all points of the sets. In this paper, following Falconer1], we first provide a basic method to estimate the lower bounds of these two classes of set densities for the self-similar s-sets satisfying the open set condition (OSC), and then obtain elementary density bounds for such fractals at all of their points. In addition, we apply the main results to the famous classical fractals and get some new density bounds. |
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| Keywords: | self-similar s-set upper convex density upper spherical density Hausdorff measure elementary density bound APPLICATION SETS BOUNDS DENSITY apply results addition fractals basic method estimate lower bounds classes densities the open set condition paper used relationship convex upper |
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