Boundedness of \(p\)-adic Hardy operators and their commutators on \(p\)-adic central Morrey and BMO spaces (Q2443705)

The third author et al.\ [Acta Math. Sin., Engl. Ser. 29, No.~1, 137--150 (2013; Zbl 1279.42023)] introduced Hardy operators in \(p\)-adic analysis. They obatined sharp estimates of these operators on \(p\)-adic weighted Lebesgue spaces and proved that the commutators generated by the \(p\)-adic Hardy operators and the central bounded mean oscillation functions are bounded on \(p\)-adic weighted Lebesgue spaces and \(p\)-adic Herz spaces. The present paper is a new contribution to the investigation of \(p\)-adic Hardy operators. Here, the authors consider the \(p\)-adic counterpart of the \(L^q\)-spaces introduced by \textit{C. B. Morrey jun.} [Trans. Am. Math. Soc. 43, No. 1, 126--166 (1938; Zbl 0018.40501; JFM 64.0460.02)] as well as of the central Morrey spaces and \(\lambda\)-central bounded mean oscillation spaces (\(\lambda \in \mathbb{R}\)) introduced by \textit{J. Alvarez} et al.\ [Collect. Math. 51, No. 1, 1--47 (2000; Zbl 0948.42013)]. Firstly, the authors get precise norms for these operators. Then they obtain sharp estimates. Finally, they discuss the boundedness for commutators generated by \(p\)-adic Hardy operators and \(\lambda\)-central bounded mean oscillation functions on \(p\)-adic central Morrey spaces.