Research proof index

Assume the phase space is countable, $a\ge4$, $1<q<2$, and every truncated Calderón-Zygmund operator $T_r$ has the required uniform strong $L^2$ bound. Then the two-sided metric Carleson operator is bounded from Lorentz $L^{q,1}$ to weak Lorentz $L^{q,\infty}$, with the explicit project constant $4C(a,q)/q$.