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Commutators and Morrey spaces. (English) Zbl 0761.42009

A locally L p function f is said to belong to the Morrey space L p,λ ( n ) if

f p,λ p =sup x,ρ ρ -λ |x-y|ρ |f(y)| p dy<·

As is known, the commutators between the Calderón-Zygmund singular integral operators and the multiplication operator by a function a(x) are bounded on L p ( n ), 1<p<, if and only if a(x) belongs to the John-Nirenberg space BMO . The authors show that the same result holds for the Morrey space, in place of L p . Commutators between a fractional integral operator and a(x) are also dealt with in the Morrey space as in the L p space.

Reviewer: K.Yabuta (Nara)

MSC:
42B20Singular and oscillatory integrals, several variables
42B25Maximal functions, Littlewood-Paley theory
42B30H p -spaces (Fourier analysis)
46E99Linear function spaces and their duals