𝒩(p, q, s)-type spaces in the unit ball of 𝑪n(I): basic properties and Hadamard gaps. Issue 6 (2nd June 2020) - Hu, Bingyang; Li, Songxiao
ABSTRACT: The purpose of this paper is to study a new class of function spaces, called N ( p, q, s ) -type spaces, in the unit ball B of C n . We establish some basic properties of this new function space, together with a characterization via Green's function, and finally, we study the Hadamard gap series in N ( p, q, s ) -type spaces. This is the first paper in a five part series. The second paper deals with the Carleson measure, while the third paper deals with several different characterizations of N ( p, q, s ) -type spaces via various norms and some applications to distance problems. Moreover, the fourth paper deals with the atomic decomposition of those functions belonging to N ( p, q, s ) -type spaces, and finally, the fifth paper deals with the Riemann–Stieltjes operators and multipliers on N ( p, q, s ) -type spaces.