Erratum for Convergence of Moving Averages of Multiparameter Superadditive Processes

Doğan Çömez

There is a typographical error in the paper [1]. It was stated there that “a process \{F_{(m,n)}\} ⊂ L_{p} is bounded if sup_{m,n≥1} \frac{1}{mn}∥F_{(m,n)}∥_{p} < ∞.” Here the exponent “p” is missing, that is, the correct definition should be: a process {F_{(m,n)}} ⊂ L_{p} is bounded if sup_{m,n≥1} \frac{1}{mn}∥F_{(m,n)}∥_{p}^{p} < ∞. With this correction, all the proofs in the paper are correct. On the other hand, it has been brought to the author’s attention that if the process is nonnegative, which is assumed in [1], this (corrected) definition of boundedness is too strong to allow non-constant superadditive processes. If, instead, the process is assumed to be strongly bounded, i.e. sup_{n≥1} ∥F_{n} −F_{n−1}∥_{p} < ∞ in the one-parameter case, then this restriction is no longer the case. Multiparameter extension is similar. Recently, the author has obtained various subsequential convergence results for strongly bounded admissible processes (see [2]), that also extend some of the results discussed in [1].

References

[1] D. Çömez, Convergence of moving averages of multiparameter superadditive processes, New York J. Math. 3A (1998), 135–148.

[2] D. Çömez, General and weighted averages of admissible superadditive processes, to appear in Illinois J. Math.

Department of Mathematics, North Dakota State University, Fargo, ND 58102 comez@plains.nodak.edu http://hypatia.math.ndsu.NoDak.edu/faculty/comez/