SOME MULTIPLIER THEOREMS FOR ANISOTROPIC HARDY SPACES——In Memory of Professor Yongsheng Sun

摘要

Let A be a symmetric expansive matrix and Hp(Rn) be the anisotropic Hardy space associated with A. For a function m in L∞(Rn), an appropriately chosen functionηin Cc∞(Rn) and j∈Z define mj(ξ) = m(Ajξ)η(ξ). The authors show that if 0 < p < 1 and mj belongs to the anisotropic non-homogeneous Herz space K1 1/p-1,p(Rn), then m is a Fourier multiplier from HP(Rn) to LP(Rn). For p = 1, a similar result is obtained if the space K1 0,1(Rn) is replaced by a slightly smaller space K(w). Moreover, the authors show that if 0 < p≥1 and if the sequence {(mj)v} belongs to a certain mixed-norm space, depending on p, then m is also a Fourier multiplier from Hp(Rn) to LP(Rn).