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2013•Journal of Nantong UniversityRequires access

Bound of Some Multi-variable Operators and Their Commutators on Generalized Morrey Space

Shen Xin-yan

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Abstract

Let ωi(x, r)(i = 1, 2) be positive measurable functions on Rn× R+, define bi-sublinear maximal operator M2and bilinear singular integral operator T. If(ω1, ω2)∈ S0, n, then the operator M2, T and their commutators with BMO functions are bounded from L p1, ω1(Rn) × L p2, ω2(Rn) to Lp, ω(Rn). Similarly, the commutators generated by the bilinear singular integral operator T with Lipschitz functions are also bounded on generalized Morrey spaces.All the results generalize the corresponding results of YE-Xiaofeng on generalized Morrey space.

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What this paper is about

Let ωi(x, r)(i = 1, 2) be positive measurable functions on Rn× R+, define bi-sublinear maximal operator M2and bilinear singular integral operator T. If(ω1, ω2)∈ S0, n, then the operator M2, T and their commutators with BMO functions are bounded from L p1, ω1(Rn) × L p2, ω2(Rn) to Lp, ω(Rn). Similarly, the commutators generated by the bilinear singular integral operator T with Lipschitz functions are also bounded on generalized Morrey spaces.All the results generalize the corresponding results of YE-Xiaofeng on generalized Morrey space.

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Available abstract

Let ωi(x, r)(i = 1, 2) be positive measurable functions on Rn× R+, define bi-sublinear maximal operator M2and bilinear singular integral operator T. If(ω1, ω2)∈ S0, n, then the operator M2, T and their commutators with BMO functions are bounded from L p1, ω1(Rn) × L p2, ω2(Rn) to Lp, ω(Rn). Similarly, the commutators generated by the bilinear singular integral operator T with Lipschitz functions are also bounded on generalized Morrey spaces.All the results generalize the corresponding results of YE-Xiaofeng on generalized Morrey space.

Key concepts: Mathematics, Sublinear function, Commutator, Lipschitz continuity, Bounded function, Operator (biology), Bilinear interpolation, Pure mathematics

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