New function spaces related to Morrey spaces and the Fourier transform (Q1697700)

Motivated by several plausible properties of the Morrey spaces \( \mathcal{M} ^p _q,\), \( 1\leq q\leq p < \infty\), the authors introduce and study different families of spaces related to (the Fourier transform) of the Morrey spaces. The first family are the Fourier-Morrey spaces, denoted by \( \mathcal{M}_{\mathcal{F} ^p _q},\), \( 1\leq p < q < \infty\), whose properties are studied in Section 2, while the second family are the spaces denoted by \( \mathcal{H}_{\mathcal{F} ^p _q}\), \( 1\leq p \leq q < \infty\), and their fundamental properties are given in Section 3. The embedding theorems between those spaces, the Lebesgue spaces, and the Besov spaces are given as well. Finally, a generalization of the Stein-Tomas-Strichartz estimate is given by using related mixed norm spaces.