TY - JOUR

T1 - Qp spaces and Dirichlet type spaces

AU - Bao, Guanlong

AU - Gögüş, Nihat Gökhan

AU - Pouliasis, Stamatis

N1 - Funding Information:
Received by the editors July 20, 2016; revised November 16, 2016. Published electronically March 9, 2017. _e corresponding author G. Bao was supported in part by China Postdoctoral Science Foundation (No. 2016M592514) and NNSF of China (No. 11371234 and No. 11526131). N. G. Göğüş and S. Pouliasis were supported by grant 113F301 from TÜBİTAK. AMS subject classification: 30H25, 31C25, 46E15. Keywords: Qp space, Dirichlet type space, Möbius invariant function space.
Publisher Copyright:
© Canadian Mathematical Society 2017.

PY - 2017/12

Y1 - 2017/12

N2 - In this paper, we show that the Möbius invariant function space Qp can be generated by variant Dirichlet type spaces Dμ, p induced by finite positive Borei measures j on the open unit disk. A criterion for the equality between the space p and the usual Dirichlet type space Dμ, p is given. We obtain a sufficient condition to construct different Dμ, p spaces and provide examples. We establish decomposition theorems for Dμ, p spaces and prove that the non-Hilbert space Qp is equal to the intersection of Hilbert spaces Dμ, p. As an application of the relation between Qp and Dμ, p spaces, we also obtain that there exist different Dμ, p spaces; this is a trick to prove the existence without constructing examples.

AB - In this paper, we show that the Möbius invariant function space Qp can be generated by variant Dirichlet type spaces Dμ, p induced by finite positive Borei measures j on the open unit disk. A criterion for the equality between the space p and the usual Dirichlet type space Dμ, p is given. We obtain a sufficient condition to construct different Dμ, p spaces and provide examples. We establish decomposition theorems for Dμ, p spaces and prove that the non-Hilbert space Qp is equal to the intersection of Hilbert spaces Dμ, p. As an application of the relation between Qp and Dμ, p spaces, we also obtain that there exist different Dμ, p spaces; this is a trick to prove the existence without constructing examples.

KW - Dirichlet type space

KW - Möbius invariant function space

KW - Qp space

UR - http://www.scopus.com/inward/record.url?scp=85035798581&partnerID=8YFLogxK

U2 - 10.4153/CMB-2017-006-1

DO - 10.4153/CMB-2017-006-1

M3 - Article

AN - SCOPUS:85035798581

SN - 0008-4395

VL - 60

SP - 690

EP - 704

JO - Canadian Mathematical Bulletin

JF - Canadian Mathematical Bulletin

IS - 4

ER -