The planar Cantor sets of zero analytic capacity and the local T(b)-theorem

By Joan Mateu, Xavier Tolsa, Joan Verdera. 2002

50 citations recorded by the source corpus.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3502f1ce895c257eed83d428bb0af8e3c331d3c9

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. Alexander Volberg
2. Fedor Nazarov
3. Sergei Treil
4. Xavier Tolsa
5. Tuomas Hytönen
6. Dachun Yang
7. Deping Ye
8. Jean Bourgain

In Mathematical Physics

1. Tuomas Hytönen
2. Alexander Volberg
3. Fedor Nazarov
4. Xavier Tolsa
5. Sergei Treil
6. Dachun Yang
7. Michael T. Lacey
8. Tao Mei

In Statistical and Nonlinear Physics

1. Sergei Treil
2. Fedor Nazarov
3. Alexander Volberg
4. Xavier Tolsa

Citations in the corpus

• The Tb-theorem on non-homogeneous spaces that proves a conjecture of Vitushkin (2014, methodology): “tion in (INV) hinders us from proving that γc ≥ Aγ+ . Recently Xavier Tolsa [XT3] used (INV) and a very clever “induction on scales” that appeared in the preprint by J. Mateu, X. Tolsa and J. Verdera [MTV], in which it is shown that the condition conjectured by Mattila characterizes the Cantor sets ”
• Painlevé's problem and the semiadditivity of analytic capacity (2002, methodology): “ we need to work with a measure “better” than ν0, which we call ν. This new measure will be a suitable modification of ν0 with the required estimate for its variation. To construct ν, we operate as in [MTV]. We consider a set Fcontaining Emade up of a finite disjoint union of squares: F= S i∈I Qi. One”