Variational estimates for averages and truncated singular integrals along the prime numbers

Mirek, Mariusz; Trojan, Bartosz; Zorin-Kranich, Pavel

doi:10.1090/tran/6822

Variational estimates for averages and truncated singular integrals along the prime numbers
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by Mariusz Mirek, Bartosz Trojan and Pavel Zorin-Kranich PDF

Trans. Amer. Math. Soc. 369 (2017), 5403-5423 Request permission

Abstract:

We prove, in a unified way, $r$-variational estimates, $r>2$, on $\ell ^{s}(\mathbb {Z})$ spaces, $s \in (1, \infty )$, for averages and truncated singular integrals along the set of prime numbers. Moreover, we obtain an improved growth rate of the bounds as $r\to 2$.

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