Weak type (1,1) estimates for noncommutative rough homogeneous singular integrals
Junming Cao, Wei Li, Lian Wu
Abstract
We establish the weak type \((1,1)\) endpoint estimate for operator-valued rough homogeneous singular integrals with kernels satisfying the classical \(L L\) integrability and cancellation conditions. This extends Seeger's endpoint theorem [J. Amer. Math. Soc. 9 (1996)] to the noncommutative setting. A key ingredient is an off-diagonal analysis that controls interactions between different kernel scales and avoids an additional logarithmic loss.
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