Ritt operators on L^1 admit bounded generalized square functions Q_{α,s,m} for α + 1 < s m, with weak type (1,1) bounds for convolution operators under conditions on the measure μ.
Cuny, On the Ritt property and weak type maximal inequalities for co nvolution powers on l1(Z)
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Square Functions and Variational Estimates for Ritt Operators on $L^1$
Ritt operators on L^1 admit bounded generalized square functions Q_{α,s,m} for α + 1 < s m, with weak type (1,1) bounds for convolution operators under conditions on the measure μ.