Nontriviality of Riesz–Morrey spaces

In this article, the authors completely answer an open question, presented in Tao et al. [A bridge connecting Lebesgue and Morrey spaces via Riesz norms. Banach J Math Anal. 2021;15(1):20], showing that Riesz–Morrey space is truly a new larger than particular with critical index. Indeed, just real interpolation of for suitable indices. Moreover, further show aforementioned inclusion also proper, namely, embedding sharp some sense, constructing two nontrivial spare functions, respectively, on Rn any given cube Q0 finite side length. The latter constructed function inspired by striking Dafni [The JNp: nontriviality duality. Funct 2018;275:577–603]. All proofs these results strongly depend exquisite geometrical analysis cubes Rn. As application, relationship between clarified all