Multipliers in the Hardy spaces $ H_p(D^m)$ with $ p\in (0,1 \rbrack $ and approximation properties of summability methods for power series

For conditions on a?number sequence are indicated ensuring that the multiplier operator is continuous in the Hardy space (here can also be a?polydisc ). Some sufficient conditions are also established. These results are used to find out the precise order of approximation of multiple power series by Bochner-Riesz means and to evaluate the -functional for a?pair of spaces related to the polyharmonic operator.