(1)

Two problems have been brought to our attention since the publication of our paper “New characterizations of Bergman spaces”, Ann. Acad. Sci. Math. 33 (2008), 87-99, which will be referred to as “the paper ” in what follows. The first issue concerns a result which we thought was well-known but was actually not quite so. The second issue concerns a lack of details in a major step of the proof of Theorem 2 in the paper. We will clarify these issues in this addendum. In addition, Kwon sent [3] to the first named author before our paper was ac-cepted for publication, but we failed to acknowledge Kwon’s paper. We wish to apologize here. Kwon’s paper [3] proves the one-dimensional case of our main re-sults for Bergman spaces with more general weights under the additional assump-tion that f(0) = 0. The one dimensional case of the Littlewood-Paley inequality can also be found in [1]. Related work for Hardy spaces on the unit ball can be found in [5]. We asserted in the paper that Lemma 9 could be found in [4]. This is not the case. The first inequality in Lemma 9