Criteria of a Two-Weight, Weak-Type Inequality in Orlicz Classes for Maximal Functions Defined on Homogeneous Spaces

Erxin Zhang ()
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Erxin Zhang: School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471000, China

Mathematics, 2024, vol. 12, issue 14, 1-11

Abstract: In this study, some new necessary and sufficient conditions for a two-weight, weak-type maximal inequality of the form φ 1 ( λ ) ∫ { x ∈ X : M f ( x ) > λ } ϱ ( x ) d μ ( x ) ≤ c ∫ X φ 2 c | f ( x ) | σ ( x ) d μ ( x ) are obtained in Orlicz classes, where M f is a Hardy–Littlewood maximal function defined on homogeneous spaces and ϱ is a weight function.

Keywords: weight; weak-type inequality; Hardy–Littlewood maximal function; Orlicz classes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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