Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces

Marcin BOWNIK, Kwok Pun Victor HO

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Abstract

Weighted anisotropic Triebel-Lizorkin spaces are introduced and studied with the use of discrete wavelet transforms. This study extends the isotropic methods of dyadic (φ-transforms of Frazier and Jawerth (1985, 1989) to non-isotropic settings associated with general expansive matrix dilations and A weights.

In close analogy with the isotropic theory, we show that weighted anisotropic Triebel-Lizorkin spaces are characterized by the magnitude of the (φ-transforms in appropriate sequence spaces. We also introduce non-isotropic analogues of the class of almost diagonal operators and we obtain atomic and molecular decompositions of these spaces, thus extending isotropic results of Frazier and Jawerth. Copyright © 2005 American Mathematical Society.
Original languageEnglish
Pages (from-to)1469-1510
JournalTransactions of the American Mathematical Society
Volume358
Issue number4
DOIs
Publication statusPublished - Apr 2006

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Citation

Bownik, M., & Ho, K.-P. (2006). Atomic and molecular decompositions of anisotropic Triebel-Lizorkin spaces. Transactions of the American Mathematical Society, 358(4), 1469-1510. doi: 10.1090/S0002-9947-05-03660-3