Sharp weak bounds for Hausdorff operators

Hausdorff operators on modulation and Wiener amalgam spaces

“…One can see [21] for the sharp characterization for the boundedness of Hausdorff operators on L p , and see [3,17] for the sharp characterization for the boundedness of Hausdorff operators on Hardy spaces H 1 and h 1 . We observe that the characterizations of boundedness of Hausdorff operator were also established in some other function spaces (see [1,6]). However, we find that these spaces have some similar properties as the L p spaces.…”

Hausdorff Operators on Modulation SpacesMp,ps

“…Among them, the sharp conditions for the boundedness of Hausdorff operator can be characterized in only few cases. One can see [3,4] for the characterization for the boundedness of Hausdorff operators on Lebesgue spaces, and see [5,6] for that on Hardy spaces 1 and ℎ 1 . There are some other results about the boundedness of Hausdorff operators on function spaces (see [7][8][9][10]).…”

Sharp weak estimates for Hardy-type operators

“…Similar weighted estimates also hold for h and h * (see [16]). Gao and Zhao in [7] obtained the sharp weak bound for H on L 1 (|x| α ) to be 1, which is independent of the dimension n and the index α. But for H * , they obtained…”