Abstrakt
Sharp weighted inequalities were recently proved for several classical operators in Harmonic analysis, however for the rough singular integral the sharp result remains open. The best bound so far was found by Hytonen, Roncal and Tapiola in [2].
For A(2) weight, it is quadratic, meaning parallel to T(Omega)f parallel to(L omega 2) = C[omega(n)](2)(3/2)parallel to f(n)parallel to(L omega n2) and [omega(n)](2) approximate to n, disproving the conjecture.