2017•Applied MathematicsOpen access

Boundedness of Calderón-Zygmund Operator and Their Commutator on Herz Spaces with Variable Exponent

Omer Abdalrhman, Afif Abdalmonem, Shuangping Tao

Abstract

The aim of this paper is to study the boundedness of Calderón-Zygmund operator and their commutator on Herz Spaces with two variable exponents ( ) ( ) ., .p q .By applying the properties of the Lebesgue spaces with variable exponent, the boundedness of the Calderón-Zygmund operator and the commutator generated by BMO function and Calderón-Zygmund operator is obtained on Herz space.

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Key concepts: Commutator, Mathematics, Operator (biology), Hardy space, Bounded mean oscillation, Maximal operator, Pure mathematics, Exponent