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Möbius invariant gradient and \(\alpha\)-Bloch functions

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Názov: Möbius invariant gradient and \(\alpha\)-Bloch functions
Autori: Zhuo, Wenxin, Pan, Yongjuan
Informácie o vydavateľovi: Zhejiang University Press, Hangzhou
Predmety: \(\alpha\)-Bloch functions, M-invariant gradient, Bloch functions, normal functions of several complex variables
Popis: Summary: Invariant gradient characterizations of \(\alpha\)-Bloch functions in the unit ball of \(\mathbb{C}^n\) are studied and it is proved that for \(f\in H(B)\), \(f\in{\mathcal B}^a\) if and only if \[ \sup_{a\in B} {1\over v(E(a,r))} \int_{E(a,r)} |\widetilde\nabla f(z)|^p(1-|z|^2)^{p(\alpha- 1)} dv(z)< \infty; \] or \[ \sup_{a\in B} \int_B(1-|z|^2)^{p(\alpha- 1)} |\widetilde\nabla f(z)|^p(1- |\varphi_a(z)|^2)^{nq} d\lambda(z)
Druh dokumentu: Article
Popis súboru: application/xml
Prístupová URL adresa: https://zbmath.org/1895014
Prístupové číslo: edsair.c2b0b933574d..26ee4b2bd60f13fa21556697a1c57afc
Databáza: OpenAIRE
Popis
Abstrakt:Summary: Invariant gradient characterizations of \(\alpha\)-Bloch functions in the unit ball of \(\mathbb{C}^n\) are studied and it is proved that for \(f\in H(B)\), \(f\in{\mathcal B}^a\) if and only if \[ \sup_{a\in B} {1\over v(E(a,r))} \int_{E(a,r)} |\widetilde\nabla f(z)|^p(1-|z|^2)^{p(\alpha- 1)} dv(z)< \infty; \] or \[ \sup_{a\in B} \int_B(1-|z|^2)^{p(\alpha- 1)} |\widetilde\nabla f(z)|^p(1- |\varphi_a(z)|^2)^{nq} d\lambda(z)