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Singular Measures and Convolution Operators

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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.

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Authors and Affiliations

  1. Departamento de Matemáticas y Computación, Universidad de La Rioja, 26004, Logroño, Spain

    J. M. Aldaz & Juan L. Varona

Authors
  1. J. M. Aldaz
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  2. Juan L. Varona
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Correspondence to Juan L. Varona.

Additional information

Research supported by Grant BFM2003–06335–C03–03 of the DGI

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Aldaz, J.M., Varona, J.L. Singular Measures and Convolution Operators. Acta Math Sinica 23, 487–490 (2007). https://doi.org/10.1007/s10114-005-0682-6

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  • DOI: https://doi.org/10.1007/s10114-005-0682-6

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