# Seminar on theory of function spaces

usually takes place Every Wednesday 10:00 Department of Mathematical Analysis, Faculty of Mathematics and Physics, Sokolovská 83
Chair: Bohumír Opic, Luboš Pick

### Endpoint estimate for rough maximal singular integral operators with rough kernels

##### Petr Honzík
Charles University
Wednesday, 27. March 2019 - 9:30 to 11:30
We show that rough maximal singular integral with kernel $\Omega(x/|x|)/|x|^n,$ $\Omega \in L^\infty,$ $\int_ {S^{n-1}} \Omega=0$ maps $L(\log \log L )^{2+\epsilon}$ to $L^{1,\inty}$ locally. This is the best known result so far, while the endpoint weak type estimate is a well known open question.