In these notes we survey some new results concerning the -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.
Keywords: $\rho $-variation, singular integral operators, uniform rectifiability.
@article{JEDP_2012____A7_0, author = {Mas, Albert}, title = {Variational inequalities for singular integral operators}, journal = {Journ\'ees \'equations aux d\'eriv\'ees partielles}, eid = {7}, pages = {1--14}, publisher = {Groupement de recherche 2434 du CNRS}, year = {2012}, doi = {10.5802/jedp.90}, language = {en}, url = {http://www.numdam.org/articles/10.5802/jedp.90/} }
TY - JOUR AU - Mas, Albert TI - Variational inequalities for singular integral operators JO - Journées équations aux dérivées partielles PY - 2012 SP - 1 EP - 14 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.90/ DO - 10.5802/jedp.90 LA - en ID - JEDP_2012____A7_0 ER -
Mas, Albert. Variational inequalities for singular integral operators. Journées équations aux dérivées partielles (2012), article no. 7, 14 p. doi : 10.5802/jedp.90. http://www.numdam.org/articles/10.5802/jedp.90/
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