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Boundedness of sublinear operators on the homogeneous Herz spaces. (English) Zbl 1043.42008

The author establishes some boundedness results for sublinear operators in homogeneous Herz spaces, which essentially improve the known results. As applications, he obtains some new conclusions about the boundedness in homogeneous Herz spaces for the higher order commutators of singular integral operators and a class of nonstandard Calderón-Zygmund operators.

MSC:

42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
47A30 Norms (inequalities, more than one norm, etc.) of linear operators
47B47 Commutators, derivations, elementary operators, etc.
47B38 Linear operators on function spaces (general)
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