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

TL;DR

This paper introduces and analyzes a new class of function spaces called $N(p, q, s)$-type spaces within the unit ball of complex n-space, exploring their properties, characterizations, and operator relations.

Contribution

It defines the $N(p, q, s)$-type spaces and investigates their fundamental properties, characterizations, and relationships with other function spaces and operators.

Findings

Established basic properties and inequalities of $N(p, q, s)$-type spaces.

Provided multiple equivalent characterizations including Carleson measures.

Characterized distances, operators, and multipliers related to these spaces.

Abstract

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