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Dive into the research topics where Albert Mas is active.

Publication


Featured researches published by Albert Mas.


arXiv: Classical Analysis and ODEs | 2012

Variation and oscillation for singular integrals with odd kernel on Lipschitz graphs

Albert Mas; Xavier Tolsa

We prove that, for r>2, the r-variation and oscillation for the smooth truncations of the Cauchy transform on Lipschitz graphs are bounded in L^p for 1<p finite. The analogous result holds for the n-dimensional Riesz transform on n-dimensional Lipschitz graphs, as well as for other singular integral operators with odd kernel. In particular, our results strengthen the classical theorem on the L^2 boundedness of the Cauchy transform on Lipschitz graphs by Coifman, McIntosh, and Meyer.


Journal of the European Mathematical Society | 2014

Variation for the Riesz transform and uniform rectifiability

Albert Mas; Xavier Tolsa

For 0 2, we prove that an n-dimensional Ahlfors-David regular measure M in R^d is uniformly n-rectifiable if and only if the r-variation for the Riesz transform with respect to M is a bounded operator in L^2(M). This result can be considered as a partial solution to a well known open problem posed by G. David and S. Semmes which relates the L^2(M) boundedness of the Riesz transform to the uniform rectifiability of M.


Communications in Mathematical Physics | 2016

An Isoperimetric-Type Inequality for Electrostatic Shell Interactions for Dirac Operators

Naiara Arrizabalaga; Albert Mas; Luis Vega

In this article we investigate spectral properties of the coupling


Siam Journal on Mathematical Analysis | 2015

Shell interactions for Dirac operators: On the point spectrum and the confinement

Naiara Arrizabalaga; Albert Mas; Luis Vega


Analysis & PDE | 2018

Klein’s paradox and the relativistic δ-shell interaction in ℝ3

Albert Mas; Fabio Pizzichillo

{H + V_\lambda}


Journal of Mathematical Physics | 2017

Dirac operators, shell interactions, and discontinuous gauge functions across the boundary

Albert Mas


Duke Mathematical Journal | 2010

A dual characterization of the

Albert Mas; Mark Melnikov; Xavier Tolsa

H+Vλ, where


Journal de Mathématiques Pures et Appliquées | 2014

{\mathcal C}^{1}

Naiara Arrizabalaga; Albert Mas; Luis Vega


Transactions of the American Mathematical Society | 2013

harmonic capacity and applications

Albert Mas

{H = -i\alpha \cdot \nabla+m\beta}


arXiv: Analysis of PDEs | 2017

Shell Interactions for Dirac Operators

Albert Mas; Fabio Pizzichillo

Collaboration


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Xavier Tolsa

Autonomous University of Barcelona

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Naiara Arrizabalaga

University of the Basque Country

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Luis Vega

University of the Basque Country

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Fabio Pizzichillo

Basque Center for Applied Mathematics

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Mark Melnikov

University of Alabama at Birmingham

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Diego Alonso-Orán

Spanish National Research Council

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Ángel D. Martínez

Spanish National Research Council

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Mark Melnikov

University of Alabama at Birmingham

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