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In this paper, we consider a new class of space, called $N(p, q, s)$-typespaces, in the unit ball $B$ of $C^n$. We study some basic properties, Hadamardgaps, Hadamard products, Random power series, Korenblum's inequality, Gleason'sproblem, atomic decomposition of $N(p, q, s)$-type spaces. Moreover, we alsoestablish several equivalent characterizations, including Carleson measurecharacterization and various derivative characterizations. Finally, we alsocharacterize the distance between Bergman-type spaces and $N(p, q, s)$-typespaces, Riemann-Stieltjes operators and multipliers on $N(p, q, s)$-typespaces.

$N(p, q, s)$-type spaces in the unit ball of $C^n$