Weighted inequalities for fractional Hardy operators and commutators

Journal of Inequalities and Applications

Dong Liu¹  Jing Liu¹  Wenming Li¹ 

[1] College of Mathematics and Information Science, Hebei Normal University;

关键词: Fractional Hardy operator;    Commutators;    One-weight inequality;    Two-weight inequality;    Maximal function;   

DOI  :  10.1186/s13660-019-2108-5

来源: DOAJ

【 摘 要 】

Abstract In this paper, we introduce a fractional maximal operators Nα $N_{\alpha }$ on (0,∞) $(0,\infty )$ associated to the fractional Hardy operator Pα $P_{\alpha }$ and its dual Qα,0≤α<1 $Q_{\alpha }, 0\leq \alpha <1$, and obtain some characterizations for the one-weight and two-weight inequalities for Nα $N_{\alpha }$. We also give some Ap $A_{p}$ type sufficient conditions for the two-weight inequalities for the fractional Hardy operators, the dual operators and the commutators of the fractional Hardy operators with CMO functions.

【 授权许可】

Unknown