Unconditional Bases for Homogeneous α-Modulation Type Spaces

Morten Nielsen*

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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 languageEnglish
Article number55
JournalMediterranean Journal of Mathematics
Issue number2
Publication statusPublished - Apr 2022

Bibliographical note

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


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


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