The Decomposition of Herz Spaces on Local Fields and Its Applications

Let 1 ≤ p ≤ ∞, 0 < l ≤ ∞, α > 0, and K be a local field. In this paper, the authors first present the unit decomposition of the Herz spaces K̇(α, p, l; K) and K(α, p, l; K). As the applications of this decomposition theory, the authors establish the K̇(α, p, l; K)- and K(α, p, l; K)-boundedness for some very general operators, and these results are sharp.