Weighted Boundedness Of Some Singular Integral Operators

The research of the boundedness of the singular integral operators and commu-tators on some function space is one of the important topics in harmonic analysis.In this thesis, we discass the boundedness of some singular integral operators.In the first chapter, applying the Dini-type condition, we prove the weightedinequality with A∞weight for the higher order commutator generated by singularintegral operator with Dini-type condition and BMO function.In the second chapter, we prove the weighted weak-type estimates with A∞weight for the commutator generated by singular integral operator with Dini-typecondition and BMO function.In the third chapter, we prove the boundedness of Calder′on-Zygmund typeoperators on weighted Herz-type Hardy spaces.Keywords: singular integral operator; Dini-type condition; weighted inequal-ity; higher order commutator; weighted weak-type estimates; commutator; Calder′on-Zygmund type operators; weighted Herz-type Hardy spaces; weighted Herz-typespaces...