New function spaces related to Morrey spaces and the Fourier transform
type: Item
instance of: scholarly article
title: New function spaces related to Morrey spaces and the Fourier transform
zbMATH Open document ID: 1387.42025
DOI: 10.1215/17358787-2017-0014
author: Shohei Nakamura
author: Yoshihiro Sawano
published in: Banach Journal of Mathematical Analysis
publication date: 2018-02-20T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.bjma/1497600064
review text: 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.
reviewed by: Nenad Teofanov
Mathematics Subject Classification ID: 42B37
Mathematics Subject Classification ID: 46B10
Mathematics Subject Classification ID: 42B35
zbMATH DE Number: 6841263
zbMATH Keywords: Morrey spaces
zbMATH Keywords: Fourier transform
zbMATH Keywords: Schrödinger propagator
zbMATH Keywords: Strichartz estimates
MaRDI profile type: Publication
OpenAlex ID: W2625499202
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description: scientific article; zbMATH DE number 6841263