Riesz means associated with certain product type convex domain

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