TY - JOUR
T1 - Intersection d'espaces de Dirichlet à poids harmonique
AU - Bao, Guanlong
AU - Göğüş, Nihat Gökhan
AU - Pouliasis, Stamatis
N1 - Funding Information:
G. Bao was supported in part by China Postdoctoral Science Foundation (No. 2016M592514) and NNSF of China (No. 11526131 and No. 11371234). N. G. G???? and S. Pouliasis were supported by grant 113F301 from T?B?TAK. The work was done while G. Bao was at Sabanci University from 01 February 2016 to 31 January 2017. It is his pleasure to acknowledge the excellent working environment provided to him there.
Publisher Copyright:
© 2017 Académie des sciences
PY - 2017/8
Y1 - 2017/8
N2 - In 1991, S. Richter introduced harmonically weighted Dirichlet spaces D(μ), motivated by his study of cyclic analytic two-isometries. In this paper, we consider ⋂μ∈PD(μ), the intersection of D(μ) spaces, where P is the family of Borel probability measures. Several function-theoretic characterizations of the Banach space ⋂μ∈PD(μ) are given. We also show that ⋂μ∈PD(μ) is located strictly between some classical analytic Lipschitz spaces and ⋂μ∈PD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.
AB - In 1991, S. Richter introduced harmonically weighted Dirichlet spaces D(μ), motivated by his study of cyclic analytic two-isometries. In this paper, we consider ⋂μ∈PD(μ), the intersection of D(μ) spaces, where P is the family of Borel probability measures. Several function-theoretic characterizations of the Banach space ⋂μ∈PD(μ) are given. We also show that ⋂μ∈PD(μ) is located strictly between some classical analytic Lipschitz spaces and ⋂μ∈PD(μ) can be regarded as the endpoint case of analytic Morrey spaces in some sense.
UR - http://www.scopus.com/inward/record.url?scp=85026826820&partnerID=8YFLogxK
U2 - 10.1016/j.crma.2017.07.013
DO - 10.1016/j.crma.2017.07.013
M3 - Article
AN - SCOPUS:85026826820
VL - 355
SP - 859
EP - 865
JO - Comptes Rendus Mathematique
JF - Comptes Rendus Mathematique
SN - 1631-073X
IS - 8
ER -