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June 13, 2026MathematicsOpen Access

Generalized Marcinkiewicz Integral Operators Along Certain Surfaces

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Authors

MAMohammed Ali

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Overview

This article confirms boundedness of generalized Marcinkiewicz operators, indicating improved results in operator theory.

Key Points

  • The aim is to establish the boundedness of rough generalized Marcinkiewicz operators using specific kernel conditions.
  • Confirmed boundedness from homogeneous Triebel–Lizorkin functions to Lp(Rd+1)
  • Utilized Yano’s extrapolation procedure for weaker kernel assumptions
  • Generalized and improved existing results in the field
  • Established boundedness of operators under singular kernel condition Lq(Sn−1)
  • Obtained appropriate Lp bounds through extrapolation
  • Extended known results leading to improved understanding of operator behavior

Cite This Study

Mohammed Ali (2026) studied this question.

synapsesocial.com/papers/6a2cf665faef96ed7f0581cdhttps://doi.org/10.3390/math14122099
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  3. 3Lp estimates for rough parametric Marcinkiewicz integrals2004
  4. 4Weighted Lp Estimates for Multiple Generalized Marcinkiewicz Functions2026
  5. 5A note on the boundedness of Marcinkiewicz integral operator on continual Herz-Morrey spaces2025 · 2 citations