Sequence spaces and stability of integer translates (Q686403)

Summary: We introduce sequence spaces of Triebel-Lizorkin type, especially Hardy spaces and bounded mean oscillation spaces. We establish \(F_ p^{\alpha q}\)-stability of integer translates of general distributions which extends the results of [\textit{R. Q. Jia}, \textit{C. A. Micchelli}, Pap. Int. Conf., Chamonix-Mont-Blanc/Fr 1990, 209-246 (1991; Zbl 0777.41013) \textit{R. Q. Jia}, \textit{J.-Z. Wang}, Proc. Am. Math. Soc. 117, No. 4, 1115-1124 (1993; Zbl 0770.42018)] to general distributions. Also the corresponding David-Journé theorem for sequences is established.