TY - JOUR
T1 - A Note on Rough Parametric Marcinkiewicz Functions
AU - Hawawsheh , Laith
AU - Al-Salman , Ahmad
AU - Momani , Shaher
JO - Analysis in Theory and Applications
VL - 1
SP - 52
EP - 59
PY - 2020
DA - 2020/05
SN - 36
DO - http://doi.org/10.4208/ata.OA-2017-0074
UR - https://global-sci.org/intro/article_detail/ata/16913.html
KW - Marcinkiewicz integrals, parametric Marcinkiewicz functions, rough kernels, Fourier transform, Marcinkiewicz interpolation theorem.
AB - <p style="text-align: justify;">In this note, we obtain sharp $L^{p}$ estimates of parametric Marcinkiewicz integral operators. Our result resolves a long standing open problem. Also, we present a class of parametric Marcinkiewicz integral operators that are bounded provided that their kernels belong to the sole space $L^{1}\left( \mathbb{S}^{n-1}\right) $.</p>