一类奇异积分算子的Toeplitz算子的双权估计  

Two weighted estimates for Toeplitz operators related to some singular integral

作　　者：曹美阳[1] 陈晓莉[1] 陈冬香[1] 

机构地区：[1]江西师范大学数学与信息科学学院,江西南昌330022

出　　处：《高校应用数学学报（A辑）》2015年第2期191-204,共14页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11261023;11461033;11401269);江西省自然科学基金(20142BAB201003)

摘　　要：研究了与满足变形L^r-Hormander条件的奇异积分算子和加权Lipschitz函数生成的Toeplitz算子T_b的sharp极大函数的点态估计,并应用该点态估计证明了Toeplitz算子T_b是从L^p(w)到L^q(w^(1-q))上的有界算子;此外还建立了与变形Lipschitz条件的奇异积分算子和加权BMO函数相关的Toeplitz算子T_b的sharp极大函数的点态估计,证明了这类Toeplitz算子是从L^p(μ)到L^q(v)上的有界算子.In this paper, the pointwise estimate for the sharp maximal function of the Toeplitz operators Tb generalized by some singular integral whose kernel satisfied some variant Lr-Hormander condition and weighted Lipschitz function is established. The authors proved that Tb is bounded from Lp（w） to Lq（w1q）. On the other hand, the pointwise estimate for the Toeplitz operator Tb generalized by weighted BMO function and singular integral with a variant Lipschitz condition kernel is also established. Meanwhile the （Lp（μ）, Lq（ν））-boundedness for Tb is also proved.

关 键 词：变形Lr-Hormander条件 变形Lipschitz条件 TOEPLITZ算子 双权估计 

分 类 号：O174.2[理学—数学]