WEAK (1,1) ESTIMATES FOR LITTLEWOOD-PALEY FUNCTIONS WITH ROUGH KERNELS

摘要

We consider Marcinkiewicz integrals on R~n and T~m arising from rough kernels satisfying the L log L-condition on S~(n-1) and prove the weak type (1,1) estimates. We also prove the weighted weak type (1,1) estimates on R~n with A_1-weights. In this case the L log L-condition is replaced by the L~q-condition with q > 1.