In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg sets in the plane. For α ∈ (0, 1], a set F in the plane is said to be an α-Furstenberg set if for each direction e there is a line segment ℓe in the direction of e for which dimH(ℓe ∩ F) ≥ α. It is well known that dimH(F) ≥ max{2α, α + 12}- and it is also known that these sets can have zero measure at their critical dimension. By looking at general Hausdorff measures Hh defined for doubling functions, that need not be power laws, we obtain finer estimates for the size of the more general h-Furstenberg sets. Further, this approach allow us to sharpen the known bounds on the dimension of classical Furstenberg sets. The main difficulty we had ...
We show that the Hausdorff dimension of $(s,t)$-Furstenberg sets is at least $s+t/2+\epsilon$, where...
Let L denote the set of Liouville numbers. For a dimension function h, we write H-h( L) for the h- d...
Simple proofs for Furstenberg sets over finite fields, Discrete Analysis 2021:22, 16 pp. A _Kakeya ...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
AbstractIn this paper we study the problem of estimating the generalized Hausdorff dimension of Furs...
For α in (0, 1], a subset E of R2 is called Furstenberg set of type α or Fα-set if for each directio...
En esta tesis se estudian dos problemas del Análisis Armónico clásico desde el punto de vista de la...
In this paper we study the behavior of the size of Furstenberg sets with respect to the size of the ...
In this survey we collect and discuss some recent results on the so called “Furstenberg set problem”...
In this paper, we show that circular $(s,t)$-Furstenberg sets in $\mathbb R^2$ have Hausdorff dimens...
The Hausdorff dimension of the set of numbers which can be written using digits 0, 1,t in base 3 is ...
In this paper, we prove the identity dimH(F)=d⋅dimH(α−1(F)) , where dimH denotes Hausdorff dimension...
We use recent advances on the discretized sum-product problem to obtain new bounds on the Hausdorff ...
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real li...
We show that the Hausdorff dimension of $(s,t)$-Furstenberg sets is at least $s+t/2+\epsilon$, where...
Let L denote the set of Liouville numbers. For a dimension function h, we write H-h( L) for the h- d...
Simple proofs for Furstenberg sets over finite fields, Discrete Analysis 2021:22, 16 pp. A _Kakeya ...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
In this paper we study the problem of estimating the generalized Hausdorff dimension of Furstenberg ...
AbstractIn this paper we study the problem of estimating the generalized Hausdorff dimension of Furs...
For α in (0, 1], a subset E of R2 is called Furstenberg set of type α or Fα-set if for each directio...
En esta tesis se estudian dos problemas del Análisis Armónico clásico desde el punto de vista de la...
In this paper we study the behavior of the size of Furstenberg sets with respect to the size of the ...
In this survey we collect and discuss some recent results on the so called “Furstenberg set problem”...
In this paper, we show that circular $(s,t)$-Furstenberg sets in $\mathbb R^2$ have Hausdorff dimens...
The Hausdorff dimension of the set of numbers which can be written using digits 0, 1,t in base 3 is ...
In this paper, we prove the identity dimH(F)=d⋅dimH(α−1(F)) , where dimH denotes Hausdorff dimension...
We use recent advances on the discretized sum-product problem to obtain new bounds on the Hausdorff ...
We provide quantitative estimates for the supremum of the Hausdorff dimension of sets in the real li...
We show that the Hausdorff dimension of $(s,t)$-Furstenberg sets is at least $s+t/2+\epsilon$, where...
Let L denote the set of Liouville numbers. For a dimension function h, we write H-h( L) for the h- d...
Simple proofs for Furstenberg sets over finite fields, Discrete Analysis 2021:22, 16 pp. A _Kakeya ...