Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

Olli Saari; Christoph Thiele

doi:10.1007/s00041-017-9575-1

Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

Olli Saari^*, Christoph Thiele

^*Corresponding author for this work

Department of Mathematics and Systems Analysis

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

1 Citation (Scopus)

Abstract

We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we obtain L ^p(R ²) → L ^p(R ²) bounds for all 1 < p< ∞. We discuss various related results.

Original language	English
Pages (from-to)	167–183
Number of pages	17
Journal	Journal of Fourier Analysis and Applications
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/s00041-017-9575-1
Publication status	Published - 15 Feb 2019
MoE publication type	A1 Journal article-refereed

Keywords

Hyperbolic cross
Maximal functions
Multipliers
Square functions

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10.1007/s00041-017-9575-1

https://arxiv.org/abs/1701.05093

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abstract = "We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we obtain L p(R 2) → L p(R 2) bounds for all 1 < p< ∞. We discuss various related results. ",

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AU - Thiele, Christoph

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AB - We study the linearized maximal operator associated with dilates of the hyperbolic cross multiplier in dimension two. Assuming a Lipschitz condition and a lower bound on the linearizing function, we obtain L p(R 2) → L p(R 2) bounds for all 1 < p< ∞. We discuss various related results.

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KW - Maximal functions

KW - Multipliers

KW - Square functions

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Lipschitz Linearization of the Maximal Hyperbolic Cross Multiplier

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Keywords

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