Equivalent descriptions and applications of $ \mathcal{Q}_K(p, q) $-type spaces in the unit ball

Mahmoud Ali Bakhit; Ali N. A. Koam; Hussain Gissy; Mahmoud Ali Bakhit; Ali N. A. Koam; Hussain Gissy

doi:10.3934/math.20261142

AIMS Mathematics

2026, Volume 11, Issue 9: 28686-28709. doi: 10.3934/math.20261142

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Equivalent descriptions and applications of $ \mathcal{Q}_K(p, q) $-type spaces in the unit ball

Department of Mathematics, Faculty of Science, Jazan University, Jazan 45142, Saudi Arabia

Received: 08 June 2026 Revised: 06 August 2026 Accepted: 24 August 2026 Published: 07 September 2026
MSC : 32A36, 32A37

The $ \mathcal{Q}_K(p, q) $-type spaces on the unit ball $ \mathbb{B} $ in $ \mathbb{C}^n $ form a broad and flexible family of function spaces that unify several classical spaces in complex analysis. In this paper, we investigate equivalent norm characterizations for these spaces and establish descriptions in terms of higher-order derivatives. As an application, we examine pointwise multipliers on $ \mathcal{Q}_K(p, q) $-type spaces and provide an explicit description of the spectrum of pointwise multipliers on $ \mathcal{Q}_K(p, q) $.
- $ \mathcal{Q}_K(p, q) $-type spaces,
- equivalent norms,
- higher-order derivatives,
- pointwise multipliers,
- spectrum
Citation: Mahmoud Ali Bakhit, Ali N. A. Koam, Hussain Gissy. Equivalent descriptions and applications of $ \mathcal{Q}_K(p, q) $-type spaces in the unit ball[J]. AIMS Mathematics, 2026, 11(9): 28686-28709. doi: 10.3934/math.20261142

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Abstract

The $ \mathcal{Q}_K(p, q) $-type spaces on the unit ball $ \mathbb{B} $ in $ \mathbb{C}^n $ form a broad and flexible family of function spaces that unify several classical spaces in complex analysis. In this paper, we investigate equivalent norm characterizations for these spaces and establish descriptions in terms of higher-order derivatives. As an application, we examine pointwise multipliers on $ \mathcal{Q}_K(p, q) $-type spaces and provide an explicit description of the spectrum of pointwise multipliers on $ \mathcal{Q}_K(p, q) $.

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