### Abstract

We prove, in a unified way, r-variational estimates, r > 2, on ℓ^{s} (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.

Original language | English (US) |
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Pages (from-to) | 5403-5423 |

Number of pages | 21 |

Journal | Transactions of the American Mathematical Society |

Volume | 369 |

Issue number | 8 |

DOIs | |

State | Published - Jan 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

*Transactions of the American Mathematical Society*,

*369*(8), 5403-5423. https://doi.org/10.1090/tran/6822

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*Transactions of the American Mathematical Society*, vol. 369, no. 8, pp. 5403-5423. https://doi.org/10.1090/tran/6822

**Variational estimates for averages and truncated singular integrals along the prime numbers.** / Mirek, Mariusz; Trojan, Bartosz; Zorin-Kranich, Pavel.

Research output: Contribution to journal › Article

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

PY - 2017/1/1

Y1 - 2017/1/1

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.

UR - http://www.scopus.com/inward/record.url?scp=85019034882&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85019034882&partnerID=8YFLogxK

U2 - 10.1090/tran/6822

DO - 10.1090/tran/6822

M3 - Article

AN - SCOPUS:85019034882

VL - 369

SP - 5403

EP - 5423

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 8

ER -