Abstract
Let s ∈ ℝ, 0 < β ≤ ∞, 0 < q, p < ∞ and –n/q < α. In this paper the authors introduce the Herz-type Triebel–Lizorkin spaces, \( K^{{\alpha ,p}}_{q} F^{s}_{\beta } {\left( {\mathbb{R}^{n} } \right)} \) and \( \dot{K}^{{\alpha ,p}}_{q} F^{s}_{\beta } {\left( {\mathbb{R}^{n} } \right)}, \)which are the generalizations of the well-known Herz-type spaces and the inhomogeneous Triebel–Lizorkin spaces. Some properties on these Herz-type Triebel–Lizorkin spaces are also given.
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The first author is partially supported by NNSF (No. 60474070) and NSF of Hunan, China (01JJY3003); the second (corresponding) author is partially supported by RFDP (No. 20020027004) and NNSF (No. 10271015) of China
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Xu, J.S., Yang, D.C. Herz-type Triebel–Lizorkin Spaces, I. Acta Math Sinica 21, 643–654 (2005). https://doi.org/10.1007/s10114-004-0424-1
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DOI: https://doi.org/10.1007/s10114-004-0424-1