Boundedness of Littlewood-Paley operators in generalized Orlicz-Campanato spaces
One knows that the Littlewood-Paley \(g\)-function \(g(f)\), Lusin area function \(S(f)\) and the Stein's function \(g_{\lambda}^{*}(f)\) are bounded on \(L^p({\mathbb R}^n)\). \textit{D. S. Kurtz} [Proc. Am. Math. Soc. 99, 657--666 (1987; Zbl 0658.42022)] and \textit{S. Wang} [Ill. J. Math. 33, No. 4, 531--541 (1989; Zbl 0671.42018)] proved the boundedness on BMO and Lipschitz spaces. The authors obtain the boundedness of these operators on generalized Orlicz-Campanato spaces \({L}^{\Phi, \phi}({\mathbb R}^n)\) where \(\Phi\) and \(\phi\) satisfy appropriate conditions.
scientific article; zbMATH DE number 5779832
scientific article