scholarly journals An improved bound for the Minkowski dimension of Besicovitch sets in medium dimension

2001 ◽  
Vol 11 (4) ◽  
pp. 773-806 ◽  
Author(s):  
I. Laba ◽  
T. Tao
Keyword(s):  
Minkowski Dimension ◽  
Besicovitch Sets

scholarly journals An Improved Bound on the Minkowski Dimension of Besicovitch Sets in ℝ 3

2000 ◽  
Vol 152 (2) ◽  
pp. 383 ◽  
Author(s):  
Nets Hawk Katz ◽  
Izabella Laba ◽  
Terence Tao
Keyword(s):  
Minkowski Dimension ◽  
Besicovitch Sets

scholarly journals Minkowski Dimension and Explicit Tube Formulas for p-Adic Fractal Strings

2018 ◽  
Vol 2 (4) ◽  
pp. 26 ◽  
Author(s):  
Michel Lapidus ◽  
Hùng Lũ’ ◽  
Machiel Frankenhuijsen
Keyword(s):  
Counting Function ◽  
Minkowski Dimension ◽  
Volume Formula ◽  
Fractal Strings ◽  
Complex Dimensions ◽  
Abscissa Of Convergence ◽  
Tubular Neighborhoods ◽  
Fractal String ◽  
Tube Formulas ◽  
Asymptotic Growth Rate

The theory of complex dimensions describes the oscillations in the geometry (spectra and dynamics) of fractal strings. Such geometric oscillations can be seen most clearly in the explicit volume formula for the tubular neighborhoods of a p-adic fractal string L p , expressed in terms of the underlying complex dimensions. The general fractal tube formula obtained in this paper is illustrated by several examples, including the nonarchimedean Cantor and Euler strings. Moreover, we show that the Minkowski dimension of a p-adic fractal string coincides with the abscissa of convergence of the geometric zeta function associated with the string, as well as with the asymptotic growth rate of the corresponding geometric counting function. The proof of this new result can be applied to both real and p-adic fractal strings and hence, yields a unifying explanation of a key result in the theory of complex dimensions for fractal strings, even in the archimedean (or real) case.

Minkowski Dimension and Cauchy Transform in Clifford Analysis

2007 ◽  
Vol 1 (3) ◽  
pp. 301-305 ◽  
Author(s):  
Ricardo Abreu Blaya ◽  
Juan Bory Reyes ◽  
Tania Moreno García
Keyword(s):  
Clifford Analysis ◽  
Cauchy Transform ◽  
Minkowski Dimension

scholarly journals Minkowski dimension of Brownian motion with drift

10.4171/jfg/4 ◽  
2014 ◽  
Vol 1 (2) ◽  
pp. 153-176 ◽  
Author(s):  
Philippe Charmoy ◽  
Yuval Peres ◽  
Perla Sousi
Keyword(s):  
Brownian Motion ◽  
Minkowski Dimension ◽  
Brownian Motion With Drift

Dimensions of weighted Besicovitch sets

2010 ◽  
Vol 26 (4) ◽  
pp. 711-716
Author(s):  
Yu Qiong Xie ◽  
Zhi Xiong Wen ◽  
Min Yu
Keyword(s):  
Besicovitch Sets

scholarly journals Differentiability inside sets with Minkowski dimension one

2016 ◽  
Vol 65 (3) ◽  
pp. 613-636 ◽  
Author(s):  
Michael Dymond ◽  
Olga Maleva
Keyword(s):  
Minkowski Dimension ◽  
Dimension One

Maximal operators associated to Fourier multipliers with an arbitrary set of parameters

1998 ◽  
Vol 128 (4) ◽  
pp. 683-696 ◽  
Author(s):  
Javier Duoandikoetxea ◽  
Ana Vargas
Keyword(s):  
Convex Body ◽  
Maximal Operator ◽  
The Body ◽  
Fourier Multipliers ◽  
Maximal Operators ◽  
Minkowski Dimension ◽  
Real Numbers ◽  
Positive Real ◽  
Multiplier Operator ◽  
Range Of Values

We present here some general results of boundedness on LP for maximal operators of the form , where E is a subset of the positive real numbers and Tt is a dilation of a fixed multiplier operator. The range of values of p depends only on the decay at infinity of the multiplier and the Minkowski dimension of E. For the case being the maximal operator associated to a convex body, we prove that the norm of the operator is independent of the body.

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