Geodesic
Boundedness of Hausdorff Operators on Hardy Spaces over Homogeneous Spaces of Lie Groups
Journal of Lie theory, Tome 31 (2021) no. 4, pp. 1015-1024
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The aim of this note is to give boundedness conditions for Hausdorff operators on Hardy spaces H1 with the norm defined via (1,q) atoms over homogeneous spaces of Lie groups with doubling property and to apply the obtained results to generalized Delsarte operators and to Hausdorff operators over multidimensional spheres.
Classification : 43A85, 47G10, 22E30
Mots-clés : Hausdorff operator, Lie group, homogeneous space, Hardy space, generalized shift operator of Delsarte 
@article{JLT_2021_31_4_JLT_2021_31_4_a7,
     author = {A. R. Mirotin},
     title = {Boundedness of {Hausdorff} {Operators} on {Hardy} {Spaces} over {Homogeneous} {Spaces} of {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {1015--1024},
     year = {2021},
     volume = {31},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2021_31_4_JLT_2021_31_4_a7/}
}
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A. R. Mirotin. Boundedness of Hausdorff Operators on Hardy Spaces over Homogeneous Spaces of Lie Groups. Journal of Lie theory, Tome 31 (2021) no. 4, pp. 1015-1024. http://geodesic.mathdoc.fr/item/JLT_2021_31_4_JLT_2021_31_4_a7/