8 citations · 8 across the 3 of their papers we have counts for
5 papers
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 vanishes, then the set of points where the principal value…
A note on a result of Saks and Zygmund on additive functions of rectangles
Julià Cufí, Juan J. Donaire
We modify the proof of the basic lemma of a paper of Saks and Zygmund on additive functions of rectangles.
Iterates of Blaschke products and Peano curves
Juan Jesús Donaire, Artur Nicolau
Let be a finite Blaschke product with which is not a rotation and let be its -th iterate. Given a sequence of complex numbers consider $F= \sum…
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…
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…