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 -