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2014•Journal of Jiangxi Normal UniversityRequires access

The Boundedness of Higher Order Commutators for the Parametric Marcinkiewicz Integral with Non-Doubling Measures

Jian Zhou

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Abstract

Under the assumption that μ only satisfies the polynomial growth condition,the( Lp( μ),Lq( μ)) boundedness of higher order commutator Mρ bf( x) generated by the parametric Marcinkiewicz integral and Lipβ( μ) function are estabished. And the boundedness on H1( μ) spaces is also obtained,which promote some results on single linear parametric Marcinkiewicz integral commutators.

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What this paper is about

Under the assumption that μ only satisfies the polynomial growth condition,the( Lp( μ),Lq( μ)) boundedness of higher order commutator Mρ bf( x) generated by the parametric Marcinkiewicz integral and Lipβ( μ) function are estabished. And the boundedness on H1( μ) spaces is also obtained,which promote some results on single linear parametric Marcinkiewicz integral commutators.

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Available abstract

Under the assumption that μ only satisfies the polynomial growth condition,the( Lp( μ),Lq( μ)) boundedness of higher order commutator Mρ bf( x) generated by the parametric Marcinkiewicz integral and Lipβ( μ) function are estabished. And the boundedness on H1( μ) spaces is also obtained,which promote some results on single linear parametric Marcinkiewicz integral commutators.

Key concepts: Commutator, Mathematics, Parametric statistics, Order (exchange), Function (biology), Pure mathematics, Polynomial, Mathematical analysis

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