Weighted vector-valued estimates for a non-standard Calderón–Zygmund operator. (December 2017)

• Record Type: Journal Article
• Authors: Hu, Guoen
• Is Part Of: Nonlinear analysis. Volume 165(2017)
• Page Start: 143
• Page End: 162
• Publication Date: 2017-12
• Subjects: 42B20; Singular integral operator -- Weighted vector-valued bound -- Ap constant -- Maximal operator -- Sparse operator; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2017.09.013
• Languages: English
• ISSNs: 0362-546X

Abstract

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 ∗ .