Singular measures and convolution operators

  1. Aldaz, J.M. 1
  2. Varona, J.L. 1
  1. 1 Universidad de La Rioja
    info

    Universidad de La Rioja

    Logroño, España

    ROR https://ror.org/0553yr311

Journal:
Acta Mechanica Sinica

ISSN: 0567-7718

Year of publication: 2007

Volume: 23

Issue: 3

Pages: 487-490

Type: Article

DOI: 10.1007/S10114-005-0682-6 SCOPUS: 2-s2.0-34047241306 WoS: WOS:000245267900011 arXiv: 0207285 GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Acta Mechanica Sinica

Institutional repository: lock_openOpen access Editor lock_openOpen access Postprint

Abstract

We show that in the study of certain convolution operators, functions can be replaced by measures without changing the size of the constants appearing in weak type (1, 1) inequalities. As an application, we prove that the best constants for the centered Hardy-Littlewood maximal operator associated with parallelotopes do not decrease with the dimension. © Springer-Verlag Berlin Heidelberg 2007.