Approximation properties of generalized Bochner-Riesz means in the Hardy spaces $H_p$, $0<p\le 1$

A test for the convergence of the generalized spherical and $\ell_1$ Bochner-Riesz means in the Hardy spaces $H_p(D^n)$, $0<p\le 1$, is obtained, where $D^n$ is the unit polydisc. Precise orders of the approximation of functions by the generalized $\ell_q$ Bochner-Riesz means in terms of the $K$-functional and special moduli of smoothness are found.
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