arXiv subjects

Jose G. Llorente

Publications and source records attributed to Jose G. Llorente.

2 recordsLinked to original sources

arXiv2012

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

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, under appropriate assumptions, the set of points where the incremental quotients are bounded has maximal Hausdorff dimension.

math.CA↗

arXiv2010

Differentiability of functions in the Zygmund class

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 similar result for functions in the Small Zygmund class is also proved and an example is constructed to show that these results are sharp.

math.CA↗