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Zeitschrift für Analysis und ihre Anwendungen

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Volume 12, Issue 3, 1993, pp. 567–584
DOI: 10.4171/ZAA/547

Published online: 1993-09-30

Sequence Spaces and Stability of Integer Translates

Qiyu Sun[1]

(1) Zhejiang University, China

In this paper, we introduce sequence spaces of Triebel-Lizorkin type, especially Hardy spaces and bounded mean oscillation spaces. We establish $F^{\alpha q}_p$-stability of integer translates of general distributions which extends the results of [7,8] to general distributions. Also the corresponding David-Journé theorem for sequences is established.

Keywords: Spaces of Triebel-Lizorkin type, stability of integer translates, David-Journé theorem, sampling theorems, global linear independence, $\Phi$-transforms, multiresolution analysis

Sun Qiyu: Sequence Spaces and Stability of Integer Translates. Z. Anal. Anwend. 12 (1993), 567-584. doi: 10.4171/ZAA/547