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Discrete harmonic analysis

2015/19/B/ST1/01149

Keywords

Descriptors

  • ST1_8: Analiza
  • ST1_3: Teoria liczb

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

Voivodeship: 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
2016-07-22
Project end date
2019-07-21
Project duration
36 months (the same as in the proposal)
Project status
Project settled

Project description

Download the project description in a pdf file

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)

  1. Jump inequalities via real interpolation

    Authors:
    Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
    Academic press:
    Mathematische Annalen (year: 2020, volume: 376, pages: 797-819), Publisher: Springer International Publishing AG
    Status:
    Published
    DOI:
    10.1007/s00208-019-01889-2 – link to the publication

  2. A bootstrapping approach to jump inequalities and their applications

    Authors:
    Mariusz Mirek, Elias M. Stein, Pavel Zorin-Kranich
    Academic press:
    Analysis & PDE (year: 2020, volume: 13, pages: 527-558), Publisher: Mathematical Sciences Publishers
    Status:
    Published
    DOI:
    10.2140/apde.2020.13.527 – link to the publication

  3. 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) (year: 2018, volume: 28, pages: 58-99), Publisher: Springer International Publishing AG,
    Status:
    Published
    DOI:
    10.1007/s00039-018-0433-3 – link to the publication

  4. 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 (year: 2019, volume: 141, pages: 587-905), Publisher: Johns Hopkins University
    Status:
    Published
    DOI:
    10.1353/ajm.2019.0023 – link to the publication

  5. 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 (year: 2020, volume: 365, pages: 107065), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2020.107065 – link to the publication

  6. Square function estimates for discrete Radon transforms

    Authors:
    Mariusz Mirek
    Academic press:
    Analysis & PDE (year: 2018, volume: 11, pages: 583-608), Publisher: Mathematical Sciences Publishers
    Status:
    Published
    DOI:
    10.2140/apde.2018.11.583 – link to the publication

  7. 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 (year: 2019, volume: 277, pages: 2471-2521), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.jfa.2018.10.020 – link to the publication

  8. 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 (year: 2017, volume: 209, pages: 665-748), Publisher: Springer Berlin Heidelberg
    Status:
    Published
    DOI:
    10.1007/s00222-017-0718-4 – link to the publication

  9. Two-parameter version of Bourgain's inequality I: Rational frequencies.

    Authors:
    Ben Krause, Mariusz Mirek, Bartosz Trojan
    Academic press:
    Advances in Mathematics (year: 2018, volume: 323, pages: 720-744), Publisher: Elsevier
    Status:
    Published
    DOI:
    10.1016/j.aim.2017.10.033 – link to the publication

Book publications / chapters in book publications (2)

  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 (year: 2020, volume: 2256, pages: 127-169), Publisher: 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 (year: 2021, volume: bd., pages: 24), Publisher: Springer Nature Switzerland AG 2020
    Status:
    Accepted for publication

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