A Modified Spanne–Peetre Inequality on Mixed Morrey Spaces

We obtain a modified version of the Spanne–Peetre inequality in the context of Morrey spaces with mixed norm. The geometric structure of the mixed Morrey spaces under consideration, dictates the new definition of Morrey–Lipschitz space. The Spanne–Peetre inequality that we find ensures that if a function belongs to a suitable Morrey space with mixed norm, then the modified integral operator which characterizes the Spanne–Peetre inequality, belongs to a suitable Morrey–Lipschitz space.