Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L es...Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.展开更多
基金The Science and Technology Research(Z2014057)of Higher Education in Hebei Provincethe Doctoral Foundation(L2015B05)of Hebei Normal Universitythe NSF(A2015403040)of Hebei Province
文摘Let L be the infinitesimal generator of an analytic semigroup on L;（R;）with pointwise upper bounds on heat kernel,and denote by L;the fractional integrals of L.For a BMO function b（x）,we show a weak type Llog L estimate of the commutators [b,L;]（f）(x) = b（x）L;（f）(x)-L;（bf）(x).We give applications to large classes of differential operators such as the Schr¨odinger operators and second-order elliptic operators of divergence form.
