| Institution: | 1.Department of Mathematics,Mudanjiang Normal University,Mudanjiang,People’s Republic of China;2.Faculty of Information Technology,Macau University of Science and Technology,Macau,People’s Republic of China |
| Abstract: | Let \(0\le \alpha <n\), \(b,M_{\alpha }]\) and \(b,M^{\sharp }]\) be the nonlinear commutators of the fractional maximal function \(M_{\alpha }\) and the sharp maximal function \(M^{\sharp }\) with a locally integrable function b. In this note, we give necessary and sufficient conditions for the boundedness of \(b,M_{\alpha }]\) and \(b,M^{\sharp }]\) on Orlicz spaces when the symbol b belongs to Lipschitz spaces, by which some new characterizations of non-negative Lipschitz functions (in terms of the Orlicz norm) are obtained. |
