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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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

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

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

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Digital Object Identifier

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

Morrey spaces Fourier transform Schrödinger propagator Strichartz estimates


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.

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