Geodesic
New $2$-microlocal Besov and Triebel--Lizorkin spaces via the Litllewood--Paley decomposition
Eurasian mathematical journal, Tome 14 (2023) no. 3, pp. 75-111

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In this paper we introduce and investigate new 2-microlocal Besov and Triebel–Lizorkin spaces via the Littlewood–Paley decomposition. We establish characterizations of these function spaces by the $\varphi$-transform, the atomic and molecular decomposition and the wavelet decomposition. As applications we prove boundedness of the the Calderón–Zygmund operators and the pseudo-differential operators on the function spaces. Moreover, we give characterizations via oscillations and differences. 
@article{EMJ_2023_14_3_a4,
     author = {K. Saka},
     title = {New $2$-microlocal {Besov} and {Triebel--Lizorkin} spaces via the {Litllewood--Paley} decomposition},
     journal = {Eurasian mathematical journal},
     pages = {75--111},
     publisher = {mathdoc},
     volume = {14},
     number = {3},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2023_14_3_a4/}
}
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K. Saka. New $2$-microlocal Besov and Triebel--Lizorkin spaces via the Litllewood--Paley decomposition. Eurasian mathematical journal, Tome 14 (2023) no. 3, pp. 75-111. http://geodesic.mathdoc.fr/item/EMJ_2023_14_3_a4/