Analytic version of critical $Q$ spaces and their properties

TL;DR

This paper introduces an analytic version of critical $Q$ spaces on the unit disc, explores their relation to Morrey spaces, and characterizes their multiplier spaces through bounded integral operators.

Contribution

It establishes a new analytic framework for critical $Q$ spaces, linking them to Morrey spaces and identifying their multiplier spaces.

Findings

Defined $Q^{eta}_{p}(bD)$ spaces on the unit disc.

Proved relations between $Q^{eta}_{p}(bD)$ and Morrey spaces.

Characterized multiplier spaces via bounded integral operators.

Abstract

In this paper, we establish an analytic version of critical spaces $Q_{\alpha}^{\beta}(\mathbb{R}^{n})$ on unit disc $\mathbb{D}$, denoted by $Q^{\beta}_{p}(\mathbb{D})$. Further we prove a relation between $Q^{\beta}_{p}(\mathbb{D})$ and Morrey spaces. By the boundedness of two integral operators, we give the multiplier spaces of $Q^{\beta}_{p}(\mathbb{D})$.