Littlewood-Paley characterizations of Triebel-Lizorkin-Morrey spaces via ball averages (Q730412)

By using the Lusin-area function and the \(g_\lambda^\star \)-function, the authors discuss equivalent characterizations of the Triebel-Lizorkin-Morrey space \(\mathcal{E}^{\alpha}_{u, p, q} ( \mathbb{R}^n )\) with smoothness order \(\alpha \in (0, 2 )\) for indices \(p, u, q \) satisfying \(1 < p \leq u < \infty \) and \( 1 < q \leq \infty \).