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1997•Bulletin of the London Mathematical SocietyRequires access

A Note on Two-Weight Inequalities for Maximal Functions and Singular Integrals

Andrea Cianchi

Open publisher page 5 citations

Abstract

We deal with weighted inequalities of the type [formula] where: T is either the Hardy–Littlewood maximal operator or a singular integral operator; G is any measurable subset of Rn; f is any measurable function, vanishing outside G, such that Tf is well-defined; v and w are weights, that is, nonnegative locally integrable functions on G; p, q∈(1, ∞). 1991 Mathematics Subject Classification 42B20, 42B25.

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What this paper is about

We deal with weighted inequalities of the type [formula] where: T is either the Hardy–Littlewood maximal operator or a singular integral operator; G is any measurable subset of Rn; f is any measurable function, vanishing outside G, such that Tf is well-defined; v and w are weights, that is, nonnegative locally integrable functions on G; p, q∈(1, ∞). 1991 Mathematics Subject Classification 42B20, 42B25.

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Available abstract

We deal with weighted inequalities of the type [formula] where: T is either the Hardy–Littlewood maximal operator or a singular integral operator; G is any measurable subset of Rn; f is any measurable function, vanishing outside G, such that Tf is well-defined; v and w are weights, that is, nonnegative locally integrable functions on G; p, q∈(1, ∞). 1991 Mathematics Subject Classification 42B20, 42B25.

Key concepts: Mathematics, Singular integral operators, Maximal operator, Maximal function, Mathematics Subject Classification, Singular integral, Operator (biology), Weight function

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