各向异性Hardy空间上的一类卷积型算子

A CLASS OF CONVOLUTION OPERATORS ON ANISOTROPIC HARDY SPACES

引入了各向异性Hardy空间上的一类卷积型算子,即带(α,r)型核的算子,0≤α<1,r为正整数.研究了这类算子作用在某些原子上的性质,并得到了一个各向异性非齐性Herz型Hardy空间到各向异性Hardy空间有界性的定理.

A class of convolution operators on anisotropic Hardy spaces, namely, convolution operators with kernels of （α,r） type are introduced. Let 0≤α〈l and r be a positive integer, and then the property of these operators acting on some atoms is studied. As an application of this property, a boundedness theorem for these operators from anisotropic non-homogeneous Herz-type Hardy space to anisotropic Hardy space is obtained.