Publication at Faculty of Mathematics and Physics |
2020
Abstract
We study the rough maximal singular integral T-Omega(#)(f)(x) = sup(epsilon>0)vertical bar integral(Rn\B(0,epsilon)) vertical bar y vertical bar(-n)Omega(y/vertical bar y vertical bar)f(x - y)dy vertical bar, where Omega is a function in L-infinity(Sn-1) with vanishing integral. It is well known that the operator is bounded on L-P for 1 < p < infinity, but it is an open question whether it is of the weak type 1-1.
We show that is bounded from L(log log L)(2+epsilon) to L-1,L-infinity locally.