The purpose of this paper is to study several different properties of the holomorphic \({\cal N}\left( {p,q,s} \right)\)-type functions in the unit ball \(\mathbb{B}\) of ℂⁿ via Carleson measure techniques. More precisely, we establish an atomic decomposition on such spaces and then we solve the Gleason’s problem on them. We also study the distance problems between Bergman-type spaces \({A^{ - {q \over p}}}\left(\mathbb{R} \right)\) and \({\cal N}\left( {p,q,s} \right)\)-type spaces. These results yield some new characterizations of the holomorphic F(p, q, t)-functions.

本文的目的是研究单位球\（\ mathbb {B}中全纯\（{\ cal N} \ left（{p，q，s} \ right）\）型函数的几种不同性质\） ℂ的^ñ经由Carleson测度技术。更确切地说，我们在此类空间上建立原子分解，然后解决它们上的格里森问题。我们还研究了Bergman型空间\（{A ^ {-{q \ over p}}} \ left（\ mathbb {R} \ right）\）和\（{\ cal N} \ left（ {p，q，s} \ right）\） -类型的空格。这些结果产生了全纯F（p，q，t）函数的一些新特征。