Unconditional Bases for Homogeneous α-Modulation Type Spaces

Morten Nielsen

doi:10.1007/s00009-022-02001-w

Unconditional Bases for Homogeneous α-Modulation Type Spaces

Morten Nielsen^*

^*Corresponding author for this work

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Abstract

We construct orthonormal bases compatible with bi-variate homogeneous α-modulation spaces and the associated spaces of Triebel–Lizorkin type. The construction is based on generating a separable α-covering and using carefully selected tensor products of univariate brushlet functions with regard to this covering. We show that the associated systems form an unconditional bases for the homogeneous α-spaces of Triebel–Lizorkin type.

Original language	English
Article number	55
Journal	Mediterranean Journal of Mathematics
Volume	19
Issue number	2
ISSN	1660-5446
DOIs	https://doi.org/10.1007/s00009-022-02001-w
Publication status	Published - Apr 2022

Bibliographical note

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© 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Keywords

Decomposition space
smoothness space
Triebel–Lizorkin type space
unconditional basis
α-modulation space

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unconditional_bases_alphamodAccepted author manuscript, 922 KB

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abstract = "We construct orthonormal bases compatible with bi-variate homogeneous α-modulation spaces and the associated spaces of Triebel–Lizorkin type. The construction is based on generating a separable α-covering and using carefully selected tensor products of univariate brushlet functions with regard to this covering. We show that the associated systems form an unconditional bases for the homogeneous α-spaces of Triebel–Lizorkin type.",

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AB - We construct orthonormal bases compatible with bi-variate homogeneous α-modulation spaces and the associated spaces of Triebel–Lizorkin type. The construction is based on generating a separable α-covering and using carefully selected tensor products of univariate brushlet functions with regard to this covering. We show that the associated systems form an unconditional bases for the homogeneous α-spaces of Triebel–Lizorkin type.

KW - Decomposition space

KW - smoothness space

KW - Triebel–Lizorkin type space

KW - unconditional basis

KW - α-modulation space

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ER -

Unconditional Bases for Homogeneous α-Modulation Type Spaces

Abstract

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Keywords

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