Banach Journal of Mathematical Analysis

New function spaces related to Morrey spaces and the Fourier transform

Shohei Nakamura and Yoshihiro Sawano

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Abstract

We introduce new function spaces to handle the Fourier transform on Morrey spaces and investigate fundamental properties of the spaces. As an application, we generalize the Stein–Tomas Strichartz estimate to our spaces. The geometric property of Morrey spaces and related function spaces will improve some well-known estimates.

Article information

Source
Banach J. Math. Anal. Volume 12, Number 1 (2018), 1-30.

Dates
Received: 25 May 2016
Accepted: 23 October 2016
First available in Project Euclid: 16 June 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1497600064

Digital Object Identifier
doi:10.1215/17358787-2017-0014

Subjects
Primary: 42B37: Harmonic analysis and PDE [See also 35-XX]
Secondary: 46B10: Duality and reflexivity [See also 46A25] 42B35: Function spaces arising in harmonic analysis

Keywords
Morrey spaces Fourier transform Schrödinger propagator Strichartz estimates

Citation

Nakamura, Shohei; Sawano, Yoshihiro. New function spaces related to Morrey spaces and the Fourier transform. Banach J. Math. Anal. 12 (2018), no. 1, 1--30. doi:10.1215/17358787-2017-0014. https://projecteuclid.org/euclid.bjma/1497600064


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