Triebel-Lizorkin-Type Spaces with Variable Exponents
By Dachun Yang, Ciqiang Zhuo, Wen Yuan. 2015
87 citations recorded by the source corpus.
In this article, the authors first introduce the Triebel-Lizorkin-type space $F_{p(\cdot),q(\cdot)}^{s(\cdot),\phi}(\mathbb R^n)$ with variable exponents, and establish its $\varphi$-transform characterization in the sense of Frazier and Jawerth, which further implies that this new scale of function spaces is well defined. The smooth molecular and the smooth atomic characterizations of $F_{p(\cdot),q(\cdot)}^{s(\cdot),\phi}(\mathbb R^n)$ are also obtained, which are used to prove a trace theorem of $F_{p(\cdot),q(\cdot)}^{s(\cdot),\phi}(\mathbb R^n)$. The authors also characterize the space $F_{p(\cdot),q(\cdot)}^{s(\cdot),\phi}(\mathbb R^n)$ via Peetre maximal functions.
Subfields: Applied Mathematics
View Paper: https://www.semanticscholar.org/paper/d9d495901163df2d3c984a87233c0a3103c539eb
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In Applied Mathematics
Citations in the corpus
- Martingale Hardy spaces with variable exponents (2014, background): “grals with nonstandard growth conditions. We also note that in the recent years more attention was turned to the study of function spaces with variable exponent in harmonic analysis; see for instance [2, 4, 5, 8, 22, 26, 30]. Let Ω ⊂ Rn. We say that a function p(·) : Ω → Ris locally log-Ho¨lder cont”
- Variable weak Hardy spaces and their applications (2016, background): “On the other hand, based on the variable Lebesgue space, several variable function spaces are developed rapidly in recent years (see, for example, [3, 4, 12, 14, 32, 41, 44, 45]).”