Zobrazeno 1 - 10
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pro vyhledávání: '"Mass transference"'
We develop the Mass Transference Principle for rectangles of Wang \& Wu (Math. Ann. 2021) to incorporate the `unbounded' setup; that is, when along some direction the lower order (at infinity) of the side lengths of the rectangles under consideration
Externí odkaz:
http://arxiv.org/abs/2410.18578
Autor:
Daviaud, Édouard
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 October 2024 538(1)
Autor:
He, Yubin
The mass transference principle, discovered by Beresnevich and Velani [Ann Math (2), 2006], is a landmark result in Diophantine approximation that allows us to obtain the Hausdorff measure theory of $\limsup$ set. Another important tool is the notion
Externí odkaz:
http://arxiv.org/abs/2402.00513
Autor:
Allen, Demi, Daviaud, Edouard
In this article we survey some recent extensions and generalisations of the celebrated Mass Transference Principle (Beresnevich and Velani, Annals of Mathematics, 2006).
Comment: 29 pages
Comment: 29 pages
Externí odkaz:
http://arxiv.org/abs/2306.15535
Autor:
Daviaud, Édouard
In this article, we prove that from any sequence of balls whose associated limsup set has full $\mu$-measure, one can extract a well-distributed subsequence of balls. From this, we deduce the optimality of various lower bounds for the Hausdorff dimen
Externí odkaz:
http://arxiv.org/abs/2204.01304
Autor:
Zhong, Wenmin
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 March 2021 495(1)
Autor:
Persson, Tomas1 tomasp@maths.lth.se
Publikováno v:
Real Analysis Exchange. 2022, Vol. 47 Issue 1, p191-205. 15p.
Publikováno v:
In Talanta 1 June 2021 228
Autor:
Persson, Tomas
I prove a mass transference principle for general shapes, similar to a recent result by H. Koivusalo and M. Rams. The proof relies on Vitali's covering lemma and manipulations with Riesz energies. The main novelty is that it is proved that the obtain
Externí odkaz:
http://arxiv.org/abs/1911.10399
Autor:
Wang, Baowei, Wu, Jun
By introducing a ubiquity property for rectangles, we prove the mass transference principle from rectangles to rectangles, i.e., if a sequence of rectangles forms a ubiquity system (a full measure property), then the limsup set defined by shrinking t
Externí odkaz:
http://arxiv.org/abs/1909.00924