Some inequalities for self-mappings of unit ball satisfying the invariant Laplacians

In this paper, we study those mappings in unit ball satisfying the Dirichlet problem of the following differential operators Delta(gamma) = (1 - |x|(2)) . [1 - |x|(2)/4 . Sigma(i) partial derivative(2)/partial derivative x(i)(2) +gamma Sigma(i) x(i) . partial derivative/partial derivative x(i) + gamma(n/2 - - gamma)]. Our aim is to establish the Schwarz type inequality, Heinz-Schwarz type inequality and boundary Schwarz inequality for those mappings.

Automated summary

In this paper, we study mappings in the unit ball that satisfy a specific differential operator condition and aim to establish corresponding inequalities.