Let K be the Calderón-Zygmund convolution kernel on R^d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R^d)by T_af(x)=p.v.∫_(R^d)K(x-y)m_x,y^a·f(y)dy,which is an extension...Let K be the Calderón-Zygmund convolution kernel on R^d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R^d)by T_af(x)=p.v.∫_(R^d)K(x-y)m_x,y^a·f(y)dy,which is an extension of the classical Calderón commutator. In this paper, we show that T_a is weighted weak type(1,1) bounded with A,1 weight for d≥2.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11371057,11471033 and 11571160)Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.20130003110003)the Fundamental Research Funds for the Central Universities (Grant No. 2014KJJCA10)
文摘Let K be the Calderón-Zygmund convolution kernel on R^d(d≥2).Christ and Journé defined the commutator associated with K and a∈L~∞(R^d)by T_af(x)=p.v.∫_(R^d)K(x-y)m_x,y^a·f(y)dy,which is an extension of the classical Calderón commutator. In this paper, we show that T_a is weighted weak type(1,1) bounded with A,1 weight for d≥2.
