It is shown that a simple closed curve in $${\mathbb {C}}^n$$ uniform limit of rectifiable curves each which has nontrivial polynomial hull itself hull. In case the rectifiable, to be hulls. also every , $$n\ge 2$$ can approximated total variation norm by polynomially convex, coincides with original except on an arbitrarily small segment. As corollary, it arc contained curve.

Following a recent paper [10] we show that the finiteness of square function associated with the Riesz transforms with respect to Hausdorff measure H (n is interger) on a set E implies that E is rectifiable.

We formalize the notion of limit an inverse system metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to sequence free Carnot groups fixed rank n and increasing step. In this case, space in correspondence signatures rectifiable paths ℝ , as introduced by Chen. Hambly-Lyons’s result on uniqueness signature implies that a geodesic tree. As particular c...

The L (1 < p < ∞) and weak-L estimates for the variation for CalderónZygmund operators with smooth odd kernel on uniformly rectifiable measures are proven. The L boundedness and the corona decomposition method are two key ingredients of the proof.

We study the asymptotic behavior of orthogonal polynomials. The measure is concentrated on a complex rectifiable arc and has an infinity of masses in the region exterior to the arc. 2000 Mathematics Subject Classification. 42C05, 30E15, 30E10.

In paper found conditions that guarantee that solution of LoewnerKufarev equation maps unit disc onto domain with quasiconformal rectifiable boundary, or it has continuation on closed unit disc, or it’s inverse function has continuation on closure of domain.

This talk will give a short introduction of how one may put a “dyadic cube” structure on spaces of homogeneous type (see Coifman-Weiss ’77) and how when this dyadic cube structure is coupled with the Whitney decomposition it allows one to construct approximating NTA domains for uniformly rectifiable (UR) sets. (The term uniformly rectifiable is quantitative, scale invariant version of rectifiab...