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Related Experiment Videos

H theory for the poly-disc.

R F Gundy1, E M Stein

  • 1Statistics Center, Rutgers University, New Brunswick, New Jersey 08903.

Proceedings of the National Academy of Sciences of the United States of America
|March 1, 1979
PubMed
Summary
This summary is machine-generated.

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This study characterizes H(p) spaces on the bi-disc using nontangential maximal functions and area integrals. Probabilistic analogues involving two-time Brownian motion and square functions are also explored.

Area of Science:

  • Harmonic Analysis
  • Function Spaces
  • Probability Theory

Background:

  • H(p) spaces are crucial in harmonic analysis.
  • Understanding their properties on the bi-disc is essential.

Purpose of the Study:

  • To characterize H(p) spaces on the bi-disc.
  • To explore connections between analytic and probabilistic methods.

Main Methods:

  • Nontangential maximal function and area integral characterizations.
  • Introduction of two-time Brownian motion (martingale maximal function).
  • Analysis of corresponding square functions.

Main Results:

  • Established characterizations of H(p) spaces using both analytic and probabilistic tools.

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  • Demonstrated the equivalence of these different characterization approaches.

    • Conclusions:

    • The study provides a comprehensive understanding of H(p) spaces on the bi-disc.
    • It highlights the power of probabilistic methods in analyzing function spaces.