A removability theorem for Sobolev functions and detour sets

Removability of Hölder Graphs for Continuous Sobolev Functions

We characterize the removability of Hölder-α graphs with respect to continuous Sobolev W 1,2 functions. For α > 2/3 these graphs are removable, while for α < 2/3 there exist graphs which are not removable.

Singular sets of Sobolev functions

Removability of Singular Sets of Harmonic Maps

We prove that a harmonic map with small energy and monotonicity property is smooth if its singular set is rectifiable and has a finite uniform density; moreover, the monotonicity property holds if the singular set has a lower dimension or its gradient has higher integrability. This work generalizes the results in [CL][DF][LG12], which were proved under the assumptions that the singular sets are...

Titchmarsh theorem for Jacobi Dini-Lipshitz functions

Our aim in this paper is to prove an analog of Younis's Theorem on the image under the Jacobi transform of a class functions satisfying a generalized Dini-Lipschitz condition in the space $mathrm{L}_{(alpha,beta)}^{p}(mathbb{R}^{+})$, $(1< pleq 2)$. It is a version of Titchmarsh's theorem on the description of the image under the Fourier transform of a class of functions satisfying the Dini-Lip...

The Riesz Transform, Rectifiability, and Removability for Lipschitz Harmonic Functions

We show that, given a set E ⊂ Rn+1 with finite n-Hausdorff measure Hn, if the n-dimensional Riesz transform