Bounds for discrete multilinear spherical maximal functions in higher dimensions

We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions d⩾5. That is, we show that this operator is bounded on lp(Zd)×lq(Zd)→lr(Zd) for 1/p+1/q⩾1/r and r>d/(d−2) and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in...

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Bibliographic Details
Published in:The Bulletin of the London Mathematical Society 2021-06, Vol.53 (3), p.855-860
Main Authors: Anderson, Theresa C., Palsson, Eyvindur Ari
Format: Article
Language:English
Subjects:
11Dxx
42Bxx (primary)
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Summary:We find the sharp range for boundedness of the discrete bilinear spherical maximal function for dimensions d⩾5. That is, we show that this operator is bounded on lp(Zd)×lq(Zd)→lr(Zd) for 1/p+1/q⩾1/r and r>d/(d−2) and we show this range is sharp. Our approach mirrors that used by Jeong and Lee in the continuous setting. For dimensions d=3,4, our previous work, which used different techniques, still gives the best known bounds. We also prove analogous results for higher degree k, ℓ‐linear operators.
ISSN:0024-6093
1469-2120
DOI:10.1112/blms.12465