Lp Estimates of certain rough parametric Marcinkiewicz functions

  • Laith Hawawsheh
  • Ahmad Al-SalmanEmail author
Research Article


We prove Lp estimates of a class of parametric Marcinkiewicz integral operators when their kernels satisfy only the \(L^1(\mathbb{S}^{n-1})\) integrability condition. The obtained Lp estimates resolve a problem left open in previous work. Our argument is based on duality technique and direct estimation of operators. As a consequence of our result, we deduce the Lp boundedness of a class of fractional Marcinkiewicz integral operators.


Marcinkiewicz integrals parametric Marcinkiewicz functions rough kernels Marcinkiewicz interpolation theorem 


42B20 42B15 42B25 


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The corresponding author acknowledges the support of Sultan Qaboos University through the grant IG/SCI/DOMS/18/01.


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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Basic Sciences and HumanitiesGerman Jordanian UniversityAmmanJordan
  2. 2.Department of MathematicsSultan Qaboos UniversityMuscatOman

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