Endpoint estimates for some maximal operators associated to the circular conical surface

For ψ∈C0∞(Rd) and m>0m>0 we consider the maximal operator given byMmf(x,t)=supr>0|∫Rdf(x−y,t−|y|m)1rdψ(yr)dy|. It is well known that MmMm is a LpLp-bounded operator for 1