Some weighted inequalities for Hausdorff operators and commutators

Abstract

In this paper, we consider the problem of boundedness of Hausdorff operator on weighted central Morrey spaces. In particular, we obtain sharp bounds for Hausdorff operators on power weighted central Morrey spaces. Analogous results for the commutators of Hausdorff operators when the symbol functions belong to weighted central-BMO spaces are obtained as well.

Weighted CBMO estimates for the commutators of matrix Hausdorff operator on Heisenberg group

“…Recently, weighted boundedness of matrix Hausdorff operators and their commutators defined on different underlying spaces are established in [34,35,36,37,38,39,40,41].…”

A characterization of two-weight norm inequalities for multidimensional Hausdorff operators on Lebesgue spaces

“…The Hausdorff operators has been extensively studied in recent years, particularly its boundedness on the Lebesgue space as well as on the Hardy space [1], [8], [9], [25], [28]- [34], [37] and [38]. We also refer to [4], [6], [7], [10]- [13], [16]- [18], [21], [22] and [35] for some recent works in this vein. Recently, two-weight inequalities in the framework of one-dimensional Hausdorff operators were studied in [4] and [31] (see, also [6]).…”

Estimates for the Commutators of p-Adic Hausdorff Operator on Herz-Morrey Spaces

“…The boundedness of the analog of H b Φ,A on R n and its special cases when A(t) = diag[1/|t|, 1/|t|, ..., 1/|t|] were discussed in [31][32][33][34][35][36][37]. However, this topic still needs further considerations in the sense of its boundedness on p-adic function spaces.…”