TY - JOUR

T1 - Variational estimates for averages and truncated singular integrals along the prime numbers

AU - Mirek, Mariusz

AU - Trojan, Bartosz

AU - Zorin-Kranich, Pavel

N1 - Funding Information:
The first and second authors were partially supported by NCN grant DEC-2012/05/D/ST1/00053. The third author was partially supported by the ISF grant 1409/11. The authors thank the Hausdorff Research Institute for Mathematics for hospitality during the trimester program “Harmonic Analysis and Partial Differential Equations”. In particular, they are greatly indebted to Christoph Thiele for his warm hospitality. The authors are grateful to the referee for a careful reading of the manuscript and useful remarks that led to the improvement of the presentation.
Publisher Copyright:
© 2017 American Mathematical Society.

PY - 2017

Y1 - 2017

N2 - We prove, in a unified way, r-variational estimates, r > 2, on ℓs (Z) spaces, s ∈ (1, ∞), for averages and truncated singular integrals along the set of prime numbers. Moreover, we obtain an improved growth rate of the bounds as r → 2.

AB - We prove, in a unified way, r-variational estimates, r > 2, on ℓs (Z) spaces, s ∈ (1, ∞), for averages and truncated singular integrals along the set of prime numbers. Moreover, we obtain an improved growth rate of the bounds as r → 2.

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U2 - 10.1090/tran/6822

DO - 10.1090/tran/6822

M3 - Article

AN - SCOPUS:85019034882

SN - 0002-9947

VL - 369

SP - 5403

EP - 5423

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 8

ER -