We prove a result related to Bressan's mixing problem. We establish an inequality for the change of Bianchini semi-norms of characteristic functions under the flow generated by a divergence free time dependent vector field. The approach leads to a bilinear singular integral operator for which we prove bounds on Hardy spaces. We include additional observations about the approach and a discrete toy version of Bressan's problem.
Mots clés : Mixing flows, Bilinear singular integrals, Bressan's mixing problem, Hardy spaces
@article{AIHPC_2018__35_4_921_0, author = {Had\v{z}i\'c, Mahir and Seeger, Andreas and Smart, Charles K. and Street, Brian}, title = {Singular integrals and a problem on mixing flows}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {921--943}, publisher = {Elsevier}, volume = {35}, number = {4}, year = {2018}, doi = {10.1016/j.anihpc.2017.09.001}, mrnumber = {3795021}, zbl = {1387.37010}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2017.09.001/} }
TY - JOUR AU - Hadžić, Mahir AU - Seeger, Andreas AU - Smart, Charles K. AU - Street, Brian TI - Singular integrals and a problem on mixing flows JO - Annales de l'I.H.P. Analyse non linéaire PY - 2018 SP - 921 EP - 943 VL - 35 IS - 4 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.anihpc.2017.09.001/ DO - 10.1016/j.anihpc.2017.09.001 LA - en ID - AIHPC_2018__35_4_921_0 ER -
%0 Journal Article %A Hadžić, Mahir %A Seeger, Andreas %A Smart, Charles K. %A Street, Brian %T Singular integrals and a problem on mixing flows %J Annales de l'I.H.P. Analyse non linéaire %D 2018 %P 921-943 %V 35 %N 4 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.anihpc.2017.09.001/ %R 10.1016/j.anihpc.2017.09.001 %G en %F AIHPC_2018__35_4_921_0
Hadžić, Mahir; Seeger, Andreas; Smart, Charles K.; Street, Brian. Singular integrals and a problem on mixing flows. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 4, pp. 921-943. doi : 10.1016/j.anihpc.2017.09.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2017.09.001/
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