Strongly singular convolution operators on the weighted Herz-type Hardy spaces

Let 0-less-than-p-less-than-or-equal-to-1-less-than-q-less-than-0, and w(1),w(2)-is-an-element-of-A(1) (Muckenhoupt-class). In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HKqalpha,p(w(1),w(2)) to the homogeneous weighted Herz spaces K-q(alpha,p)(w(1),w(2)), provided alpha=n(1-1/q). Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HKqalpha,p(w(1),w(2)) is also investigated.