Application of general approach to the theory of Morrey-type spaces. (English) Zbl 1466.46017
Summary: In this paper, we generalize constructions of Morrey spaces by using as a basic space a general rearrangement invariant space \(E(\mathbb R^n)\) instead of \(L_p((\mathbb R^n)\) and a general ideal space \(F((\mathbb R_+)\) for outer norm instead of \(L_\infty((\mathbb R_+)\) or \(L_{q, w}((\mathbb R_+)\). Embeddings, nontriviality conditions, and inclusion into a general concept of ideal spaces and generalized rearrangement invariant spaces are discussed.
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 47A30 | Norms (inequalities, more than one norm, etc.) of linear operators |
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