We consider the notion of a signed magic array, which is an m × n rectangular array with the same number of filled cells s in each row and the same number of filled cells t in each column, filled with a certain set of numbers that is symmetric about the number zero, such that every row and column has a zero sum. We attempt to make progress toward a characterization of for which (m, n, s, t) there exists such an array. This characterization is complete in the case where n = s and in the case where n = m; we also characterize three-fourths of the cases where n = 2m.

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We prove the weighted L p regularity of the ordinary Bergman projection on certain pseudoconvex domains where the weight belongs to an appropriate generalization of the Bekollé-Bonami class. The main tools used are estimates on the Bergman kernel obtained by McNeal and Bekollé's original approach of proving a good-lambda inequality.