Porosities and Dimensions of Measures Satisfying the Doubling Condition
نویسنده
چکیده
This paper explains the implications of a mathematical theory (by the same authors) of holes in fractals and their relation to dimension for measurements. The novelty of our approach is to consider the fractal measure on a set rather than just the support of that measure. This should take into account in a more precise way the distribution of data points in measured sets, such as the distribution of galaxies.
منابع مشابه
Porosities and Dimensions of Measures
University of Geneva, Departments of Physics and Mathematics, 1211 Geneva 4, Switzerland University of Jyväskylä, Department of Mathematics, P.O. Box 35, FIN-40351 Jyväskylä, Finland [email protected], [email protected], and [email protected] Abstract. We introduce a concept of porosity for measures and study relations between dimensions and porosities for two classes of measure...
متن کاملSharp Inequalities for Maximal Functions Associated with General Measures
Sharp weak type (1, 1) and L p estimates in dimension one are obtained for uncentered maximal functions associated with Borel measures which do not necessarily satisfy a doubling condition. In higher dimensions uncentered maximal functions fail to satisfy such estimates. Analogous results for centered maximal functions are given in all dimensions.
متن کاملThe John - Nirenberg type inequality for non - doubling measures
X. Tolsa defined the space of type BMO for a positive Radon measure satisfying some growth condition on R. This space is very suitable for the CalderónZygmund theory with non-doubling measures. Especially, the John-Nirenberg type inequality remains true. In this paper we introduce the localized and weighted version of this inequality and, as an application, we obtain some vector-valued inequali...
متن کاملSharp maximal inequalities and commutators on Morrey spaces with non-doubling measures
In this paper, related to RBMO, we prove the sharp maximal inequalities for the Morrey spaces with the measure μ satisfying the growth condition. As an application we obtain the boundedness of commutators for these spaces.
متن کاملMultilinear Analysis on Metric Spaces
The multilinear Calderón–Zygmund theory is developed in the setting of RD-spaces, namely, spaces of homogeneous type equipped with measures satisfying a reverse doubling condition. The multiple-weight multilinear Calderón–Zygmund theory in this context is also developed in this work. The bilinear T1-theorems for Besov and Triebel–Lizorkin spaces in the full range of exponents are among the main...
متن کامل