Discrete multilinear maximal functions and number theory. (English) Zbl 07783564
Many multilinear discrete operators are primed for pointwise decomposition; such decompositions give structural information but also an essentially optimal range of bounds. In this paper, the authors study the (continuous) slicing method of E. Jeong and S. Lee [J. Funct. Anal. 279, No. 7, Article ID 108629, 28 p. (2020; Zbl 1445.42006)] – which when debuted instantly gave sharp multilinear operator bounds – in the discrete setting. Via several examples, number theoretic connections, pointed commentary, and a unified theory, this useful technique maybe lead to further applications. This work generalizes, and was inspired by, the author’s work with Palsson on a special case.
Reviewer: Ciqiang Zhuo (Jena)
MSC:
| 11K70 | Harmonic analysis and almost periodicity in probabilistic number theory |
| 11P32 | Goldbach-type theorems; other additive questions involving primes |
| 42B25 | Maximal functions, Littlewood-Paley theory |
Keywords:
multilinear maximal functionsCitations:
Zbl 1445.42006References:
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