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Elementary density bounds for self-similar sets and application

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Analysis in Theory and Applications

Abstract

Falconer[1] used the relationship between upper convex density and upper spherical density to obtain elementary density bounds for s-sets at H s-almost all points of the sets. In this paper, following Falconer[1], 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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Authors and Affiliations

  1. School of Mathematics and Computer Science, Gannan Teachers College, Ganzhou, 341000, P. R. China

    Shaoyuan Xu

  2. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R China

    Weiyi Su

Authors
  1. Shaoyuan Xu
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  2. Weiyi Su
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Correspondence to Shaoyuan Xu.

Additional information

Supported in part by the Foundations of the Jiangxi Natural Science Committee (No: 0611005), China.

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Xu, S., Su, W. Elementary density bounds for self-similar sets and application. Anal. Theory Appl. 23, 334–342 (2007). https://doi.org/10.1007/s10496-007-0334-z

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  • DOI: https://doi.org/10.1007/s10496-007-0334-z

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