Transference of Hp-multipliers and their maximal functions on product domains

The aim of this paper is to establish de Leeuw type [K. de Leeuw, Ann. of Math. 81 (1965) 364– 379] and Kenig–Tomas type [C.E. Kenig, P.A. Tomas, Studia Math. 68 (1989) 79–83] transference theorems for multipliers and maximal operators defined by multipliers on the multi-parameter Hardy spaces Hp(Rn) and Hp(Dn), where 0