On Marcinkiewicz Integrals

Dear Colleagues,

Marcinkiewicz integral operators belong to the broad class of Littlewood–Paley g-functions. The L^p bounds for them are useful in the study of the smoothness properties of the functions and behavior of integral transformations, such as Poisson integrals, singular integrals and, more generally, singular Radon transforms.

The study of  Marcinkiewicz integral operators has attracted the attention of many authors, dating back to the study of such operators by A. Zygmund on the circle and by E. Stein on Euclidean n-space. Recent efforts in dealing with these operators have been mostly focused on finding the weakest possible conditions on the kernel functions under which the boundedness of these operators holds.

This Special Issue, entitled “On Marcinkiewicz Integrals”, is devoted to collecting research papers on the recent progress on Marcinkiewicz integrals. We invite high-quality original research papers, as well as survey papers related to the topic of this Special Issue.

We look forward to your contributions.

Best wishes,
Prof. Dr. Hussain Al-Qassem
Guest Editor

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• marcinkiewicz integrals
• littlewood–paley g-functions
• L^p boundedness
• rough kernels