Riesz means associated with certain product type convex domain

In this paper we study the maximal operators T⁎δ and the convolution operators TδTδ associated with multipliers of the form(1−max{|ξ0|,|ξ1|,…,|ξn−2|})+δ,(ξ0,ξ1,…,ξn−2)∈R2×Rn−2,n⩾3. We prove that T⁎δ satisfies the sharp weak type (p,p)(p,p) inequality on Hp(Rn)Hp(Rn) when 2(n−1)2n−1n(1p−1)+12. We also obtain that TδTδ is bounded from Lp(Rn)Lp(Rn) to Lp(Rn)Lp(Rn) for δ>max{2|1p−12|−12,0} and 1⩽p<∞1⩽p<∞. The indicated ranges of parameters p and δ cannot be improved.