Quantitative weighted estimates for rough homogeneous singular integrals

  1. Hytönen, T.P. 3
  2. Roncal, L. 2
  3. Tapiola, O. 1
  1. 1 Basque Center for Applied Mathematics
    info

    Basque Center for Applied Mathematics

    Bilbao, España

  2. 2 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    GRID grid.119021.a

  3. 3 University of Helsinki
    info

    University of Helsinki

    Helsinki, Finlandia

    GRID grid.7737.4

Journal:
Israel Journal of Mathematics

ISSN: 0021-2172

Year of publication: 2017

Volume: 218

Issue: 1

Pages: 133-164

Type: Article

Export: RIS
DOI: 10.1007/s11856-017-1462-6 SCOPUS: 2-s2.0-85015747736 WoS: 000398070100007 GOOGLE SCHOLAR

Metrics

Cited by

  • Scopus Cited by: 37 (12-06-2021)

Journal Citation Reports

  • Year 2017
  • Journal Impact Factor: 0.744
  • Best Quartile: Q2
  • Area: MATHEMATICS Quartile: Q2 Rank in area: 135/310 (Ranking edition: SCIE)

SCImago Journal Rank

  • Year 2017
  • SJR Journal Impact: 1.253
  • Best Quartile: Q1
  • Area: Mathematics (miscellaneous) Quartile: Q1 Rank in area: 56/439

CiteScore

  • Year 2017
  • CiteScore of the Journal : 1.3
  • Area: Mathematics (all) Percentile: 64

Abstract

We consider homogeneous singular kernels, whose angular part is bounded, but need not have any continuity. For the norm of the corresponding singular integral operators on the weighted space L2(w), we obtain a bound that is quadratic in A2 constant [w]A2. We do not know if this is sharp, but it is the best known quantitative result for this class of operators. The proof relies on a classical decomposition of these operators into smooth pieces, for which we use a quantitative elaboration of Lacey's dyadic decomposition of Dini-continuous operators: the dependence of constants on the Dini norm of the kernels is crucial to control the summability of the series expansion of the rough operator. We conclude with applications and conjectures related to weighted bounds for powers of the Beurling transform. © 2017, Hebrew University of Jerusalem.