摘要
Let 0【p≤1q【0, and w<sub>1</sub>, w<sub>2</sub> ∈A<sub>1</sub> （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HK<sub>q</sub><sup>α,p</sup>（w<sub>1</sub>; w<sub>2</sub>） to the homogeneous weighted Herz spaces K<sub>q</sub><sup>α,p</sup>（w<sub>1</sub>;w<sub>2</sub>）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HK<sub>q</sub><sup>α,p</sup>（w<sub>1</sub>, w<sub>2</sub>） is also investigated.
Let 0<p≤1q<0, and w<sub>1</sub>, w<sub>2</sub> ∈A<sub>1</sub> （Muckenhoupt-class）. In this paper the authors prove that the strongly singular convolution operators are bounded from the homogeneous weighted Herz-type Hardy spaces HK<sub>q</sub><sup>α,p</sup>（w<sub>1</sub>; w<sub>2</sub>） to the homogeneous weighted Herz spaces K<sub>q</sub><sup>α,p</sup>（w<sub>1</sub>;w<sub>2</sub>）, provided α=n（1--1/q）. Moreover, the boundedness of these operators on the non-homogeneous weighted Herz-type Hardy spaces HK<sub>q</sub><sup>α,p</sup>（w<sub>1</sub>, w<sub>2</sub>） is also investigated.
基金
the National Natural Science Foundation of China
