Carmelo Puliatti

collaborators

2 papers

math.CA2025

On Fourier transforms of fractal measures on the parabola

Tuomas Orponen, Carmelo Puliatti, Aleksi PyÃ¶rÃ¤lÃ¤

Let $s \in [0, 1]$ and $t \in [0, min {3 s, s + 1})$ . Let $I ¨ $ be a Borel measure supported on the parabola $P = {(x, x^{2}) : x \in [- 1, 1]}$ satisfying the $s$ -dimensional…

math.AP2025

Layer potentials for elliptic operators with DMO-type coefficients: big pieces $T b$ theorem, quantitative rectifiability, and free boundary problems

Andrea Merlo, Mihalis Mourgoglou, Carmelo Puliatti

For $n \geq 2$ , we consider the operator $L_{A} = - div (A (\cdot) \nabla)$ , where $A$ is a uniformly elliptic $(n + 1) \times (n + 1)$ matrix with variable coefficients, a Radon mea…

On Fourier transforms of fractal measures on the parabola

Layer potentials for elliptic operators with DMO-type coefficients: big pieces Tb theorem, quantitative rectifiability, and free boundary problems

Layer potentials for elliptic operators with DMO-type coefficients: big pieces $T b$ theorem, quantitative rectifiability, and free boundary problems