Martí Prats

activity

20142020

most citedA T(P) theorem for Sobolev spaces on domains

26 citations · 84 across the 8 of their papers we have counts for

collaborators

12 papers

math.CA2020★ 1 cited

Triebel-Lizorkin regularity and bi-Lipschitz maps: composition operator and inverse function regularity

Martí Prats

We study the stability of Triebel-Lizorkin regularity of bounded functions and Lipschitz functions under bi-Lipschitz changes of variables and the regularity of the inverse functio…

math.AP2019

Minimizers for the thin one-phase free boundary problem

Max Engelstein, Aapo Kauranen, Martí Prats +2

We consider the "thin one-phase" free boundary problem, associated to minimizing a weighted Dirichlet energy of the function in $R_{+}^{n + 1}$ plus the area of the positivity…

math.CA2019

The two-phase problem for harmonic measure in VMO

Martí Prats, Xavier Tolsa

Let $Ω^{+} \subset R^{n + 1}$ be an NTA domain and let $Ω^{-} = R^{n + 1} ∖ Ω^{+}$ be an NTA domain as well. Denote by $ω^{+}$ and $ω^{-}$ their respective harmoni…

math.AP2019★ 1 cited

Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale

Kari Astala, Martí Prats, Eero Saksman

We study quasiconformal mappings in planar domains $Ω$ and their regularity properties described in terms of Sobolev, Bessel potential or Triebel-Lizorkin scales. This leads to opt…

math.CA2018★ 8 cited

Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences

Martí Prats

In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space $F_{p, q}^{s} (Ω)$ in terms of first-order differences in a uniform domain $Ω$ . The characteri…

math.AP2017★ 2 cited

Characterization for stability in planar conductivities

Daniel Faraco, Martí Prats

We find a complete characterization for sets of isotropic conductivities with stable recovery in the $L^{2}$ norm when the data of the Calderón Inverse Conductivity Problem is obtain…

math.CA2016★ 9 cited

Sharp bounds for composition with quasiconformal mappings in Sobolev spaces

Marcos Oliva, Martí Prats

Let $ϕ$ be a quasiconformal mapping, and let $T_{ϕ}$ be the composition operator which maps $f$ to $f \circ ϕ$ . Since $ϕ$ may not be bi-Lipschitz, the composition operator need not map…

math.AP2016

Beltrami equations in the plane and Sobolev regularity

Martí Prats

New results regarding the Sobolev regularity of the principal solution of the linear Beltrami equation $\partial ˉ f = μ \partial f + ν \partial f$ for discontinuous B…

math.CA2015★ 16 cited

Sobolev regularity of the Beurling transform on planar domains

Martí Prats

Consider a Lipschitz domain $Ω$ and the Beurling transform of its characteristic function $B χ_{Ω} (z) = - p.v. \frac{1}{π z ^{2}} * χ_{Ω} (z)$ . It is shown that if the outward un…

math.CA2015

Sobolev regularity of quasiconformal mappings on domains

Martí Prats

Consider a Lipschitz domain $Ω$ and a measurable function $μ$ supported in $Ω$ with $∥ μ ∥_{L^{\infty}} < 1$ . Then the derivatives of a quasiconformal solution of t…

math.CA2015★ 21 cited

A T(1) theorem for fractional Sobolev spaces on domains

Martí Prats, Eero Saksman

Given any uniform domain $Ω$ , the Triebel-Lizorkin space $F_{p, q}^{s} (Ω)$ with $0 < s < 1$ and $1 < p, q < \infty$ can be equipped with a norm in terms of first order differences restricted t…

math.CA2014★ 26 cited

A T(P) theorem for Sobolev spaces on domains

Martí Prats, Xavier Tolsa

Recently, V. Cruz, J. Mateu and J. Orobitg have proved a T(1) theorem for the Beurling transform in the complex plane. It asserts that given $0 < s \leq 1$ , $1 < p < \infty$ with $s p > 2$ an…