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arXiv · 2406.02705

Lorentz Herz-type Besov-Triebel-Lizorkin spaces

Douadi Drihem
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Abstract

In this paper, we introduce a new family of function spaces of Besov and Triebel-Lizorkin type. We present the $\varphi $-transform characterization of these spaces in the sense of Frazier and Jawerth and we prove their Sobolev and Franke-Jewarth embeddings. Also, we establish the smooth atomic, molecular and wavelet decomposition of these function spaces. Characterizations by ball means of differences are given. Finally, we investigate a series of examples which play an important role in the study of function spaces of Besov-Triebel-Lizorkin type.

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Douadi Drihem. 2024-06-04. Lorentz Herz-type Besov-Triebel-Lizorkin spaces. https://arxiv.org/abs/2406.02705

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