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April 3, 2026Open Access

Lp estimates for rough parametric Marcinkiewicz integrals

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Authors

HAH. M. Al-Qassem

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Implication

We demonstrate Lp boundedness of certain parametric Marcinkiewicz operators, indicating improved mathematical understanding.

Key Points

  • The study aims to establish Lp boundedness for parametric Marcinkiewicz integral operators under specific conditions.
  • Proved Lp boundedness for operators M,h and related operators M*,h,M,h,S.
  • Analyzed integrability conditions on h within block space B(0,-1/2)q(Sn-1).
  • Extended previous known results regarding rough parametric Marcinkiewicz integrals.
  • Demonstrated new Lp boundedness results for specific classes of Marcinkiewicz integral operators.
  • Established necessary integrability conditions that enhance existing theories.
  • Provided significant extensions to previously known mathematical properties.

Cite This Study

H. M. Al-Qassem (2004) studied this question.

synapsesocial.com/papers/69cf58fd5a333a8214609cb7https://doi.org/10.20604/00001149
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