Weighted vector-valued estimates for a non-standard Calderón–Zygmund operator. (December 2017) - Hu, Guoen
Abstract: In this paper, the author considers the weighted vector-valued estimates for the operator defined by T A f ( x ) = p . v . ∫ R n Ω ( x − y ) | x − y | n + 1 ( A ( x ) − A ( y ) − ∇ A ( y ) ) f ( y ) d y, and the associated maximal singular integral operator T A ∗, where Ω is homogeneous of degree zero, has vanishing moment of order one, A is a function in R n such that ∇ A ∈ BMO ( R n ) . By pointwise estimates for ‖ { T A f k ( x ) } ‖ l q and ‖ { T A ∗ f k ( x ) } ‖ l q, the author obtains some quantitative weighted vector-valued bounds for T A and T A ∗ .