Abstract
We study \(L^p\) improving estimates and continuity properties of maximal operators for generalized spherical means. Once these features are obtained, they are applied to get sparse bounds on lacunary and full generalized spherical averages.
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Acknowledgements
The authors are immensely grateful to Professor Luz Roncal for the suggested ideas and the careful reading of the manuscript. The authors thank the referee for pointing out the corrections in detail. The first-named author was supported by Inspire Faculty Fellowship (DST/INSPIRE/04/2016/000776).
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Communicated by Sundaram Thangavelu.
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Bagchi, S., Hait, S. & Senthil Raani, K.S. \({\varvec{L^p-L^q}}\) estimates for generalized spherical averages. Proc Math Sci 132, 35 (2022). https://doi.org/10.1007/s12044-022-00683-6
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DOI: https://doi.org/10.1007/s12044-022-00683-6