Year: 2026
Type: article
Abstract: Let $$0 0 < p < ∞ and $$\Psi : [0,1) \rightarrow (0,\infty )$$ Ψ : [ 0 , 1 ) → ( 0 , ∞ ) , and let $$\mu $$ μ be a finite positive Borel measure on the unit disk $${\mathbb {D}}$$ D of the complex plane. We define the Lebesgue-Zygmund space $$L^p_{\mu ,\Psi }$$ L μ , Ψ p as the space of all measurable functions f on $${\mathbb {D}}$$ D such that $$\int _{{\mathbb {D}}}|f(z)|^p\Psi (|f(z)|)\,d\mu (z)<\infty $$ ∫ D | f ( z ) | p Ψ ( | f ( z ) | ) d μ ( z ) < ∞ . The weighted Bergman-Zygmund space $$A^p_{\omega ,\Psi }$$ A ω , Ψ p induced by a weight function $$\omega $$ ω consists of analytic functions in $$L^p_{\mu ,\Psi }$$ L μ , Ψ p with $$d\mu =\omega \,dA$$ d μ = ω d A . Let $$0 0 < q <
Author: Atte Pennanen
Institution: University of Eastern Finland
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W4416610259