Sharp estimates of p-adic hardy and Hardy-Littlewood-Pólya operators

Boundedness ofp-Adic Hardy Operators and Their Commutators onp-Adic Central Morrey and BMO Spaces

“…In the following, we will estimate and , respectively. For , since H is bounded from (Q ) to (Q ), 1 < < ∞ [32], then, by Hölder's inequality ( / 1 + / 2 = 1), we get…”

“…Remark 7. When = 0, the space CBMO , (Q ) is just CBMO (Q ), which is defined in [32]. If 1 ≤ 1 < 2 < ∞, by Hölder's inequality,…”

“…In [31], Fu et al obtained the precise norm of -linear Hardy operators on weighted Lebesgue spaces and central Morrey spaces. Fu et al [32] introduced -adic Hardy operators and got the sharp estimates of -adic Hardy operators on -adic weighted Lebesgue spaces. Moreover, they proved that the commutators generated by the -adic Hardy operators and the central BMO functions are bounded on -adic weighted Lebesgue spaces and -adic Herz spaces see; [33] for more information about Herz spaces.…”

Weighted Estimates for Commutator of Roughp-Adic Fractional Hardy Operator on Weightedp-Adic Herz–Morrey Spaces

“…was defined and studied for f ∈ L loc 1 (Q n p ) and 0≤α < n in [15]. When α � 0, the operator H p α transfers to the p-adic Hardy operator (see [30] for more details). Fu et al in [30] acquired the optimal bounds of p-adic Hardy operator on L q (Q n p ).…”

Sharp estimates for the p-adic Hardy type operators on higher-dimensional product spaces

“…In 2012, Fu et al [ 16 ] defined the following n -dimensional p -adic Hardy operator: where f is a nonnegative measurable function on , is a ball in with center at and radius , and they proved the sharp estimates of the p -adic Hardy operator on Lebesgue spaces with power weights.…”