Multilinear Hausdorff operators and their best constants

Some estimates for Hausdorff operators

“…In some cases, these conditions are also necessary and the corresponding operator norms are worked out. We extend and improve some known results in [6,11].Mathematics subject classification (2010): 26D10, 26D15, 42B35, 46E30. …”

Hausdorff operators on the power weighted Hardy spaces

“…A convolution operator is defined in connection to the translation, while the Hausdorff operator is raised from the dilation. Additionally, many classical operators in analysis are special cases of the Hausdorff operator if one chooses suitable kernel functions Φ (see [2,3,4,7,22]). These operators include the Hardy operator, the adjoint Hardy operator [5,8,9] and the Cesàro operator [13,23], among many others.…”

The WeightedLpandBMOEstimates for Fractional Hausdorff Operators on the Heisenberg Group

“…It is well known that many classical operators in harmonic analysis are special cases of Hausdorff operators if one chooses suitable Φ (see, for example, [1,[6][7][8][9][10]), including Hardy operators and Cesàro operator [11][12][13][14].…”