Banach Journal of Mathematical Analysis· 2026Q1
Carleson measures for weighted Bergman–Zygmund spaces
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- 2026year
Short summary
This paper characterizes bounded and compact embeddings between weighted Bergman–Zygmund spaces, defining these spaces using a measure $\mu$ and a weight function $\Psi$.
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Key points
- Defines Lebesgue–Zygmund spaces $L^p_{\mu, \Psi}$ using a measure $\mu$ and a weight function $\Psi(|f|)$.
- Defines weighted Bergman–Zygmund spaces $A_{\omega, \Psi}^p$ as analytic functions within $L^p_{\mu, \Psi}$ where $d\mu = \omega dA$.
- Characterizes bounded and compact embeddings between these spaces: $A_{\omega, \Psi}^p \subset L_{\mu, \Phi}^q$.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract For $$0 0 < p < ∞ , $$\Psi :[0,\infty )\rightarrow (0,\infty )$$ Ψ : [ 0 , ∞ ) → ( 0 , ∞ ) and a finite positive Borel measure $$\mu $$ μ on the unit disc $$\mathbb {D}$$ D , the Lebesgue–Zygmund space $$L^p_{\mu ,\Psi }$$ L μ , Ψ p consists of all measurable functions f such that $$\Vert f \Vert _{L_{\mu , \Psi }^{p}}^p =\int _{\mathbb {D}}|f|^p\Psi (|f|)\,d\mu < \infty $$ ‖ f ‖ L μ , Ψ p p = ∫ D | f | p Ψ ( | f | ) d μ < ∞ . For an integrable radial function $$\omega $$ ω on $$\mathbb {D}$$ D , the corresponding weighted Bergman-Zygmund space $$A_{\omega , \Psi }^{p}$$ A ω , Ψ p is the set of all analytic functions in $$L_{\mu , \Psi }^{p}$$ L μ , Ψ p with $$d\mu =\omega \,dA$$ d μ = ω d A . The purpose of the paper is to characterize bounded (and compact) embeddings $$A_{\omega ,\Psi }^{p}\subset L_{\mu , \Phi }^{q}$$
The authors' abstract, as published at the source. Banach Journal of Mathematical Analysis, 2026 · DOI ↗
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