Intersection of harmonically weighted Dirichlet spaces

Bao, Guanlong; Göğüş, Nıhat Gökhan; Pouliasis, Stamatis

doi:10.1016/j.crma.2017.07.013

Comptes Rendus. Mathématique

2017

DOI: 10.1016/j.crma.2017.07.013

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Intersection of harmonically weighted Dirichlet spaces

Guanlong Bao

Nıhat Gökhan Göğüş

Stamatis Pouliasis

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2019

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Cited by 1 publication

References 15 publications

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The Range of the Cesàro Operator Acting on

Bao¹,

Wulan²,

Ye³

2019

Can. Math. Bull.

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In 1993, N. Danikas and A. G. Siskakis showed that the Cesàro operator ${\mathcal{C}}$ is not bounded on $H^{\infty }$ ; that is, ${\mathcal{C}}(H^{\infty })\nsubseteq H^{\infty }$ , but ${\mathcal{C}}(H^{\infty })$ is a subset of $BMOA$ . In 1997, M. Essén and J. Xiao gave that ${\mathcal{C}}(H^{\infty })\subsetneq {\mathcal{Q}}_{p}$ for every $0<p<1$ . In this paper, we characterize positive Borel measures $\unicode[STIX]{x1D707}$ such that ${\mathcal{C}}(H^{\infty })\subseteq M({\mathcal{D}}_{\unicode[STIX]{x1D707}})$ and show that ${\mathcal{C}}(H^{\infty })\subsetneq M({\mathcal{D}}_{\unicode[STIX]{x1D707}_{0}})\subsetneq \bigcap _{0<p<\infty }{\mathcal{Q}}_{p}$ by constructing some measures $\unicode[STIX]{x1D707}_{0}$ . Here, $M({\mathcal{D}}_{\unicode[STIX]{x1D707}})$ denotes the Möbius invariant function space generated by ${\mathcal{D}}_{\unicode[STIX]{x1D707}}$ , where ${\mathcal{D}}_{\unicode[STIX]{x1D707}}$ is a Dirichlet space with superharmonic weight induced by a positive Borel measure $\unicode[STIX]{x1D707}$ on the open unit disk. Our conclusions improve results mentioned above.

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The Range of the Cesàro Operator Acting on

Bao¹,

Wulan²,

Ye³

2019

Can. Math. Bull.

View full text Add to dashboard Cite

show abstract

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Intersection of harmonically weighted Dirichlet spaces

Cited by 1 publication

References 15 publications

The Range of the Cesàro Operator Acting on

The Range of the Cesàro Operator Acting on

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