Hardy type estimates for commutators of fractional integrals
Inspired by \textit{Y. Sun} and \textit{W. Su} [J. Funct. Anal. 234, No. 2, 235--260 (2006; Zbl 1156.42306)], the authors obtain sufficient conditions for the boundedness of commutator operators \[ [b,I_\alpha](f)(x):=b(x)\,I_\alpha(f)(x)-I_\alpha(bf)(x) \] (\(b\) being from \(BMO(\mathbb R^n)\) or \(LMO(\mathbb R^n)\)) from the local Hardy spaces \(h^p(\mathbb R^n)\) into spaces \(h^p_q(\mathbb R^n):=h^p(\mathbb R^n)+L^q(\mathbb R^n)\), where \(0<\alpha<n\), \(q>n/(n-\alpha)\), \(n/(n+\alpha)<p<1\) or \(p=1\), associated with the fractional integral \[ I_\alpha f(x):=\int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha}}\,dy. \]
scientific article; zbMATH DE number 5858894
scientific article