各向异性H^P(R^n)上的乘子定理(英文)

SOME MULTIPLIER THEOREMS FOR NON-ISOTROPIC H^P(R^n)

记t＞0且1=α1≤α2≤…≤αn·设At=diag（t(α1)…，t(αn)）是Rn\｛0｝上各向异性连续交换群．对L∞（Rn）中的函数m，以及适当选取的中的函数η和任意的δ＞0，定义mδ（ξ）=m（Aδξ）η（ξ）．证明了当0＜P＜1，且属于各向异性的Herz空间时，m是各向异性HP（Rn）上的乘子．进一步，当p=1时，如果将替换成一个稍小的空间K（ω），得到了类似的结论．

Let At =diag(tα1, '', tαn) with t>0 and 1=α1≤α2≤...≤αn. be continuous groups ofnon - isotropic transformations of Rn\{0}. For a function m∈L∞ (Rn), an appropriately choen function (Rn) and any δ>0, define mδ(ξ)=m(Aδξ)η(ξ). The authers show that if 0<p<1, γ= andbelongs to the non-isotropic Herz space (Rn), then m is a Fouriermultiplier of the non- isotropic Hardy space HP(Rn). Moreover, for p=1, the authors obtain a similar theorem if the space (Rn) is replaced by a slightlysmaller space K(ω).