Multipliers With Besov Regularity On Anisotropic Hardy Spaces

The main purpose of this paper is to establish,using the Littlewood-Paley-Stein theory(in particular,the Littlewood-Paley-Stein square function),a Baernstein-Sawyer type theorem for the following Fourier multipliers on anisotropic Hardy spaces Hp(Rn;A)associated with expensive dilation A:Assume that m(ξ)is a function on Rn satisfing with s=ζ--1(1/p-1/2).We proof that Tm is bounded from Hp(Rn;A)to Hp(Rn;A)for all 0<p<1 and where A*denotes the transpose of A.Here we have used the notations mj=m(A*jξ)φ(ξ)and φ(ξ)is a suitable cut-off function on Rn,and B2,1s(A*)is an anistropic Besov space associated with expansive dilation A*on Rn.