Characterizations of Hardy spaces for Fourier integral operators

Jan Rozendaal

doi:10.4171/rmi/1246

Characterizations of Hardy spaces for Fourier integral operators

Jan Rozendaal^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

We prove several characterizations of the Hardy spaces for Fourier integral operators Hp FIO(Rn), for 1 < p < 1. First we characterize Hp FIO(Rn) in terms of Lp(Rn)-norms of parabolic frequency localizations. As a corollary, any characterization of Lp(Rn) yields a corresponding version for Hp FIO(Rn). In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions.

Original language	English
Pages (from-to)	1717-1745
Number of pages	29
Journal	Revista Matematica Iberoamericana
Volume	37
Issue number	5
DOIs	https://doi.org/10.4171/rmi/1246
Publication status	Published - 2021

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title = "Characterizations of Hardy spaces for Fourier integral operators",

abstract = "We prove several characterizations of the Hardy spaces for Fourier integral operators Hp FIO(Rn), for 1 < p < 1. First we characterize Hp FIO(Rn) in terms of Lp(Rn)-norms of parabolic frequency localizations. As a corollary, any characterization of Lp(Rn) yields a corresponding version for Hp FIO(Rn). In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions.",

keywords = "Characterizations, Fourier integral operators, Hardy spaces, Maximal functions, Square functions",

author = "Jan Rozendaal",

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T1 - Characterizations of Hardy spaces for Fourier integral operators

AU - Rozendaal, Jan

PY - 2021

Y1 - 2021

N2 - We prove several characterizations of the Hardy spaces for Fourier integral operators Hp FIO(Rn), for 1 < p < 1. First we characterize Hp FIO(Rn) in terms of Lp(Rn)-norms of parabolic frequency localizations. As a corollary, any characterization of Lp(Rn) yields a corresponding version for Hp FIO(Rn). In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions.

AB - We prove several characterizations of the Hardy spaces for Fourier integral operators Hp FIO(Rn), for 1 < p < 1. First we characterize Hp FIO(Rn) in terms of Lp(Rn)-norms of parabolic frequency localizations. As a corollary, any characterization of Lp(Rn) yields a corresponding version for Hp FIO(Rn). In particular, we obtain a maximal function characterization and a characterization in terms of vertical square functions.

KW - Characterizations

KW - Fourier integral operators

KW - Hardy spaces

KW - Maximal functions

KW - Square functions

UR - https://www.scopus.com/pages/publications/85103863960

U2 - 10.4171/rmi/1246

DO - 10.4171/rmi/1246

M3 - Article

SN - 0213-2230

VL - 37

SP - 1717

EP - 1745

JO - Revista Matematica Iberoamericana

JF - Revista Matematica Iberoamericana

IS - 5

ER -

Characterizations of Hardy spaces for Fourier integral operators

Abstract

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