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2012•Chinese Annals of MathematicsRequires access

Estimate of Some Kind of Commutators on Generalized Morrey Spaces

Xiaofeng Ye

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Abstract

Letω_i(x,r)(i=1,2) be a positive measurable function in R~n×R~+.If(ω_1,ω_2)∈S_(0,n),then the commutators generated by the BMO function and maximal operators M are bounded from L~(p,ω_1)(R~n) to L~(p,ω_2)(R~n).Similarly,the commutators generated by the singular integral operator T and the Riesz potential operator I_αare also bounded on generalized Morrey spaces.All the results generalize the corresponding results of Mizuhara on the generalized Morrey spaces.

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What this paper is about

Letω_i(x,r)(i=1,2) be a positive measurable function in R~n×R~+.If(ω_1,ω_2)∈S_(0,n),then the commutators generated by the BMO function and maximal operators M are bounded from L~(p,ω_1)(R~n) to L~(p,ω_2)(R~n).Similarly,the commutators generated by the singular integral operator T and the Riesz potential operator I_αare also bounded on generalized Morrey spaces.All the results generalize the corresponding results of Mizuhara on the generalized Morrey spaces.

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Available abstract

Letω_i(x,r)(i=1,2) be a positive measurable function in R~n×R~+.If(ω_1,ω_2)∈S_(0,n),then the commutators generated by the BMO function and maximal operators M are bounded from L~(p,ω_1)(R~n) to L~(p,ω_2)(R~n).Similarly,the commutators generated by the singular integral operator T and the Riesz potential operator I_αare also bounded on generalized Morrey spaces.All the results generalize the corresponding results of Mizuhara on the generalized Morrey spaces.

Key concepts: Mathematics, Bounded function, Operator (biology), Pure mathematics, Singular integral, Function (biology), Riesz transform, Bounded mean oscillation

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