Abstract
A classical observation of Riesz says that truncations of a general [Formula: see text] in the Hardy space [Formula: see text] do not converge in [Formula: see text]. A substitute positive result is proved: these partial sums always converge in the Bergman norm [Formula: see text]. The result is extended to complete Reinhardt domains in [Formula: see text]. A new proof of the failure of [Formula: see text] convergence is also given.
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