What question did this study set out to answer?

The study aims to explore the boundedness properties of multilinear Calderón-Zygmund integral operators and their commutators on generalized variable exponent Morrey spaces.

April 3, 2026Open Access

Multilinear Calderón-Zygmund integral operators with generalized kernels and their commutators on product of generalized variable exponent Morrey spaces

Key Points

The study aims to explore the boundedness properties of multilinear Calderón-Zygmund integral operators and their commutators on generalized variable exponent Morrey spaces.
Analysis of operators on product variable exponent Morrey spaces
Assessment of commutators formed by functions in BMO
Establishing boundedness conditions based on the properties of the kernels
Proved that the operators are bounded from the product Morrey spaces to different Morrey target spaces.
Demonstrated boundedness of the commutator T_{\vec{b}} on the same product Morrey spaces.
Obtained a corollary confirming the boundedness of the commutator in variable exponent L spaces.

Abstract

The aim of this paper is to investigate the boundedness of a multilinear Calder? n-Zygmund integral operators with generalized kernels T and its commutator T₁ formed by b (BMO (Rⁿ) ) ᵐ and the T on product of generalized variable exponent Morrey spaces M^p₁ () ₁ (Rⁿ) M^p₂ () ₂ (Rⁿ) M^pₘ () ₘ (Rⁿ). Under assumption that the Lebesgue measurable satisfies ₁ ₂ ₘ =, the authors prove that the T is bounded from the product of generalized variable exponent Morrey spaces M^p₁ () ₁ (Rⁿ) M^p₂ () ₂ (Rⁿ) M^pₘ () ₘ (Rⁿ) to spaces M^p () (Rⁿ), and also bounded from the product variable exponent Morrey spaces L^p₁ () (Rⁿ) L^p₂ () ' (Rⁿ) L^pₘ () '' (Rⁿ) into spaces L^p () (Rⁿ). Moreover, the authors show that T₁ is bounded from the product spaces M^p₁ () ₁ (Rⁿ) M^p₂ () ₂ (Rⁿ) M^pₘ () ₘ (Rⁿ) to spaces M^p () (Rⁿ). As a corollary, the boundedness of T₁ on spaces L^p () (Rⁿ) is also obtained

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