Abstract
We consider the boundedness of Hausdorff operators on the real Hardy spaces \(H^{1}\) over double coset spaces of locally compact groups with the local doubling property and approximate midpoint property. The \(L^{q}\) spaces as well as the example of the group of Euclidean motions are also considered.
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Notes
Real Hardy spaces over compact connected (not necessary quasi-metric) Abelian groups were defined in [21].
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Acknowledgements
The author is indebted to Prof. R. Daher for posing the problem and to the anonymous referee for useful suggestions.
Funding
The author is partially supported by the State Program of Scientific Research of Republic of Belarus, project no. 20211776. and by the Ministry of Education and Science of Russia, agreement no. 075-02-2022-893.
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Mirotin, A.R. HAUSDORFF OPERATORS OVER DOUBLE COSET SPACES OF GROUPS WITH LOCALLY DOUBLING PROPERTY. J Math Sci 266, 933–943 (2022). https://doi.org/10.1007/s10958-022-06174-3
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DOI: https://doi.org/10.1007/s10958-022-06174-3