J. J. Donaire

activity

20102023

most citedDifferentiability of functions in the Zygmund class

8 citations · 8 across the 3 of their papers we have counts for

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4 papers · 1 filter

math.CA2023

Existence of principal values of some singular integrals on Cantor sets, and Hausdorff dimension

J. Cufí, J. J. Donaire, P. Mattila +1

Consider a standard Cantor set in the plane of Hausdorff dimension 1. If the linear density of the associated measure $μ$ vanishes, then the set of points where the principal value…

math.CA2021

Iterates of Blaschke products and Peano curves

Juan Jesús Donaire, Artur Nicolau

Let $f$ be a finite Blaschke product with $f (0) = 0$ which is not a rotation and let $f^{n}$ be its $n$ -th iterate. Given a sequence ${a_{n}}$ of complex numbers consider $F= \sum…

math.CA2012

Boundary values of harmonic gradients and differentiability of Zygmund and Weierstrass functions

Juan J. Donaire, Jose G. Llorente, Artur Nicolau

We study differentiability properties of Zygmund functions and series of Weierstrass type in higher dimensions. While such functions may be nowhere differentiable, we show that, un…

math.CA2010★ 8 cited

Differentiability of functions in the Zygmund class

Juan Jesus Donaire, Jose G. Llorente, Artur Nicolau

We prove that the Hausdorff dimension of the set of points where a function in the Zygmund class in the euclidean space has bounded divided differences, is bigger or equal to 1. A…