Weighted Lp Estimates for Multiple Generalized Marcinkiewicz Functions
Year: 2026
Type: article
Abstract: In this paper we investigate the weighted Lp boundedness of generalized Marcinkiewicz integrals MK(ε) over multiple symmetric domains. Under the conditions K∈Lq(Sm−1×Sn−1), q>1, we establish suitable weighted Lp bounds for the integrals MK(ε). These bounds are combined with Yano’s extrapolation argument to obtain the weighted Lp boundedness of MK(ε) from the Triebel–Lizorkin space F.p0,ε(ω1,ω2) to the space Lp(ω1,ω2) under the weaker conditions K∈Bq(0,2ε−1)(Sm−1×Sn−1)∪L(logL)2/ε(Sm−1×Sn−1). Our findings are essential improvements and extension of several known findings in the literature.
Source: Symmetry
DOI: 10.3390/sym18020239
Authors: Mohammed Ali, Hussain Al-Qassem
Institutions: Jordan University of Science and Technology, Qatar University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,896
OpenAlex ID: W7126083762