2005•Acta Scientiarum Naturalium Universitatis SunyatseniRequires access

ON THE COMMUTATORS OF SINGULAR INTEGRAL OPERATORS

胡国恩

Abstract

Lp(Rn) (1＜p＜∞) boundedness and a weak type endpoint estimate are considered for the commutators of singular integral operators. A condition on the associated kernel is given under which the L2(Rn) boundedness of the singular integral operators implies the Lp(Rn) boundedness (1＜p＜∞) and the weak type (H1(Rn), L1(Rn))boundedness for the corresponding commutators. A new interpolation theorem is also established.

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Key concepts: Singular integral operators, Mathematics, Singular integral, Commutator, Singular integral operators of convolution type, Type (biology), Kernel (algebra), Fourier integral operator