  In this paper, we study Bohr's inequality and refined versions of
Bohr-Rogosinski inequalities involving Schwarz functions. Moreover, we
establish a version of multidimensional analogue of Bohr inequality and
Bohr-Rogosinski inequalities involving Schwarz functions. Finally, we establish
a multidimensional analogue of the refined version of Bohr inequalities with
the initial coefficient being zero. All the results are proved to be sharp.
