Weighted composition operators between  vector-valued   Bloch-type spaces

Kobra ESMAEILI; Hakimeh MAHYAR

Makale detayları

Weighted composition operators between vector-valued Bloch-type spaces

Yazarlar:

Kobra ESMAEILI | Hakimeh MAHYAR

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.151-171

Belge Tipi:

Makale

Yayın Tarihi:

1/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745680

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098

Özet:

 

Let XXX and YYY be complex Banach spaces and DD\mathbb{D} be  the open unit disc in the complex plane CC\mathbb{C}.   Let φφ\varphi  be an analytic self-map of DD\mathbb{D} and  ψψ\psi be an analytic operator-valued function from DD\mathbb{D} into the space of all bounded linear operators from XXX to Y.Y.Y.  The weighted composition operator  Wψ,φ:H→H(D,Y)Wψ,φ:H→H(D,Y)W_{\psi,\varphi}:\mathcal{H} \rightarrow\mathcal{H}(\mathbb{D}, Y)  is defined by   Wψ,φ(f)(z)=ψ(z)(f(φ(z))),(z∈D,f∈H),Wψ,φ(f)(z)=ψ(z)(f(φ(z))),(z∈D,f∈H), W_{\psi,\varphi}( f)(z)=\psi(z)(f(\varphi(z))), \quad \quad (z\in\mathbb{D}, f\in \mathcal{H}),  where HH\mathcal{H} is  the space of all analytic  XXX-valued functions on DD\mathbb{D}.  In this paper we provide necessary and sufficient conditions for the boundedness  and compactness of weighted composition operators  Wψ,φWψ,φW_{\psi,\varphi}  between  vector-valued  Bloch-type spaces Bα(X)Bα(X)\mathcal{B}_{\alpha}\left( X\right) and Bβ(Y)Bβ(Y)\mathcal{B}_{\beta}\left( Y\right) for α,β>0α,β>0\alpha, \beta >0  in terms of ψ,φψ,φ\psi,\varphi, their derivatives, and the nnnth power φnφn\varphi^n of φφ\varphi.

Makale detayları

Weighted composition operators between vector-valued Bloch-type spaces

Yazarlar: Kobra ESMAEILI | Hakimeh MAHYAR

Yayıncı: TUBITAK

Dergi: Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.151-171

Belge Tipi: Makale

Yayın Tarihi: 1/2019

Belge Dili: Türkçe

Document ID (Org No.): 2000745680

Sıklık: İki Aylık

eISSN: 1303-6149

pISSN: 1300-0098

Sayı

Yazarlar:

Kobra ESMAEILI | Hakimeh MAHYAR

Yayıncı:

TUBITAK

Dergi:

Turkish Journal of Mathematics 2019 Vol.43 Issue 1, pp.151-171

Belge Tipi:

Makale

Yayın Tarihi:

1/2019

Belge Dili:

Türkçe

Document ID (Org No.):

2000745680

Sıklık:

İki Aylık

eISSN:

1303-6149

pISSN:

1300-0098