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Distribution function inequalities for singular integrals.

R R Coifman1

  • 1Mathematics Department, Washington University, St. Louis, Missouri 63130.

Proceedings of the National Academy of Sciences of the United States of America
|October 1, 1972
PubMed
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This study establishes distribution function inequalities for maximal functions and singular integral operators. These findings advance the understanding of operator theory in mathematical analysis.

Area of Science:

  • Mathematical Analysis
  • Harmonic Analysis
  • Operator Theory

Background:

  • Maximal functions and singular integral operators are fundamental tools in harmonic analysis.
  • Understanding their behavior and inequalities is crucial for various mathematical applications.

Purpose of the Study:

  • To derive novel distribution function inequalities involving maximal functions.
  • To explore the relationship between maximal functions and singular integral operators through these inequalities.

Main Methods:

  • Utilizing techniques from real analysis and functional analysis.
  • Applying established methods for bounding maximal operators and singular integrals.

Main Results:

  • Established new inequalities for the distribution functions of maximal operators.

Related Experiment Videos

  • Demonstrated connections between the properties of singular integral operators and their associated maximal functions.

    • Conclusions:

    • The derived inequalities provide deeper insights into the behavior of these operators.
    • These results contribute to the ongoing development of harmonic analysis and its applications.