𝒬K Spaces of Several Real Variables

Abstract

We introduce a new space, ${𝒬}_K({ℝ}^n)$ space, of several real variables with nondecreasing functions $K$. By giving basic properties of the weighted function $K$, by establishing a Stegenga-type estimate, and by introducing the $K$-Carleson measure on ${ℝ}_{+}^{n+\mathrm{1}}$, we obtain various characterizations of ${𝒬}_K({ℝ}^n)$ space.