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L bounds for rough parabolic maximal operators.

Mohammed Ali1, Qutaibeh Katatbeh1

  • 1Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110, Jordan.

Heliyon
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Summary

This study establishes new estimates for rough parabolic maximal functions, improving existing results in harmonic analysis. These findings advance the understanding of functions related to surfaces of revolution.

Keywords:
ExtrapolationMathematicsParabolic maximal operatorsRough kernelsSurfaces of revolution

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Area of Science:

  • Harmonic Analysis
  • Partial Differential Equations
  • Geometric Measure Theory

Background:

  • Rough parabolic maximal functions are important operators in harmonic analysis.
  • Understanding their properties is crucial for various mathematical fields.
  • Previous results had limitations in scope and applicability.

Purpose of the Study:

  • To establish new estimates for a specific class of rough parabolic maximal functions.
  • To extend and improve upon existing results in the field.
  • To investigate functions related to surfaces of revolution.

Main Methods:

  • Development of novel analytical techniques.
  • Application of extrapolation arguments.
  • Analysis of functions associated with surfaces of revolution.

Main Results:

  • Establishment of new estimates for rough parabolic maximal functions.
  • Demonstration of the effectiveness of the extrapolation argument.
  • Improvement and extension of previously known results.

Conclusions:

  • The established estimates provide a significant advancement in the analysis of rough parabolic maximal functions.
  • The findings have implications for extending and refining results in related areas of mathematics.
  • This work opens new avenues for research in harmonic analysis and partial differential equations.