Projects funded by the NCN

Information on the principal investigator and host institution

Information of the project and the call

Keywords

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Discrete harmonic analysis

2015/19/B/ST1/01149

Keywords:

Maximal functions singular integrals variational norms ergodic theorems Littlewood-Paley square function Hardy-Littlewood circle method Vinogradov mean value theorem

Descriptors:

  • ST1_8: Analysis
  • ST1_3: Number theory

Panel:

ST1 - Mathematics: all areas of mathematics, pure and applied, as well as mathematical foundations of computer science, physics and statistics

Host institution :

Uniwersytet Wrocławski, Wydział Matematyki i Informatyki

woj. dolnośląskie

Other projects carried out by the institution 

Principal investigator (from the host institution):

dr Mariusz Mirek 

Number of co-investigators in the project: 3

Call: OPUS 10 - announced on 2015-09-15

Amount awarded: 149 760 PLN

Project start date (Y-m-d): 2016-07-22

Project end date (Y-m-d): 2019-07-21

Project duration:: 36 months (the same as in the proposal)

Project status: Project settled

Project description

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Note - project descriptions were prepared by the authors of the applications themselves and placed in the system in an unchanged form.

Information in the final report

  • Publication in academic press/journals (9)
  • Book publications / chapters in book publications (2)
  1. Dimension-free estimates for discrete Hardy-Littlewood averaging operators over the cubes in Zd
    Authors:
    Jean Bourgain, Mariusz Mirek, Elias M. Stein, Błażej Wróbel
    Academic press:
    American Journal of Mathematics (rok: 2019, tom: 141, strony: 587-905), Wydawca: Johns Hopkins University
    Status:
    Published
    DOI:
    10.1353/ajm.2019.0023 - link to the publication
  2. Jump inequalities via real interpolation
    Authors:
    Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
    Academic press:
    Mathematische Annalen (rok: 2020, tom: 376, strony: 797-819), Wydawca: Springer International Publishing AG
    Status:
    Published
    DOI:
    10.1007/s00208-019-01889-2 - link to the publication
  3. Square function estimates for discrete Radon transforms
    Authors:
    Mariusz Mirek
    Academic press:
    Analysis & PDE (rok: 2018, tom: 11, strony: 583-608), Wydawca: Mathematical Sciences Publishers
    Status:
    Published
    DOI:
    10.2140/apde.2018.11.583 - link to the publication
  4. A bootstrapping approach to jump inequalities and their applications
    Authors:
    Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
    Academic press:
    Analysis & PDE (rok: 2020, tom: 13, strony: 527-558), Wydawca: Mathematical Sciences Publishers
    Status:
    Published
    DOI:
    10.2140/apde.2020.13.527 - link to the publication
  5. On dimension free variational inequalities for averaging operators in R^d
    Authors:
    Jean Bourgain, Mariusz Mirek, Elias M. Stein, Błażej Wróbel
    Academic press:
    Geometric And Functional Analysis (GAFA) (rok: 2018, tom: 28, strony: 58-99), Wydawca: Springer International Publishing AG,
    Status:
    Published
    DOI:
    10.1007/s00039-018-0433-3 - link to the publication
  6. L^p-estimates for discrete operators of Radon type: Maximal functions and vector-valued estimates
    Authors:
    Mariusz Mirek, Elias M. Stein, Bartosz Trojan
    Academic press:
    Journal of Functional Analysis (rok: 2019, tom: 277, strony: 2471-2521), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.020 - link to the publication
  7. L^p(Z^d)-estimates for discrete operators of Radon type: Variational estimates.
    Authors:
    Mariusz Mirek, Elias M. Stein, Bartosz Trojan
    Academic press:
    Inventiones Mathematicae (rok: 2017, tom: 209, strony: 665-748), Wydawca: Springer Berlin Heidelberg
    Status:
    Published
    DOI:
    10.1007/s00222-017-0718-4 - link to the publication
  8. Two-parameter version of Bourgain's inequality I: Rational frequencies.
    Authors:
    Ben Krause, Mariusz Mirek, Bartosz Trojan
    Academic press:
    Advances in Mathematics (rok: 2018, tom: 323, strony: 720-744), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.033 - link to the publication
  9. Jump inequalities for translation-invariant operators of Radon type on Zd
    Authors:
    Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
    Academic press:
    Advances in Mathematics (rok: 2020, tom: 365, strony: 107065), Wydawca: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2020.107065 - link to the publication
  1. On discrete Hardy-Littlewood maximal functions over the balls in Zd: dimension-free estimates
    Authors:
    Jean Bourgain, Mariusz Mirek, Elias M. Stein, Błażej Wróbel
    Book:
    Geometric Aspects of Functional Analysis Israel Seminar (GAFA) 2017-2019 (rok: 2020, tom: 2256, strony: 127-169), Wydawca: Springer Nature Switzerland AG 2020
    Status:
    Published
  2. On the Hardy-Littlewood maximal functions in high dimensions: Continuous and discrete perspective
    Authors:
    Jean Bourgain, Mariusz Mirek, Elias M. Stein, Błażej Wróbel
    Book:
    Geometric Aspects of Harmonic Analysis, INdAM-Springer Series (rok: 2021, tom: bd., strony: 24), Wydawca: Springer Nature Switzerland AG 2020
    Status:
    Accepted for publication

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