Estimates for the composition of the carathéodory and homotopy operators
Department of Mathematics and System Science, National University of Defense Technology, Changsha, P.R. China
Journal of Inequalities and Applications 2012, 2012:188 doi:10.1186/1029-242X-2012-188Published: 31 August 2012
In the present paper, we deal with the composition of carathéodory and homotopy operators for differential forms satisfying the A-harmonic equation in the bounded and convex domain. We obtain estimates for the composition and the form of inequalities with weights. Moreover, we also obtain the composition for the gradient, carathéodory, and homotopy operators. Then we obtain the norm estimates for the composition operators.