Variational inequalities for singular integral operators

Mas, Albert

Journées équations aux dérivées partielles (2012), article no. 7, 14 p.

In these notes we survey some new results concerning the $\rho$-variation for singular integral operators defined on Lipschitz graphs. Moreover, we investigate the relationship between variational inequalities for singular integrals on AD regular measures and geometric properties of these measures. An overview of the main results and applications, as well as some ideas of the proofs, are given.

Classification : 42B20, 42B25
Mots clés : $\rho $-variation, singular integral operators, uniform rectifiability.

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