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Generalized integral type Hilbert operator acting between weighted Bloch spaces.
- Source :
-
Mathematical Methods in the Applied Sciences . Nov2023, Vol. 46 Issue 17, p18458-18472. 15p. - Publication Year :
- 2023
-
Abstract
- Let μ$$ \mu $$ be a finite Borel measure on [0,1)$$ \left[0,1\right) $$. In this paper, we consider the generalized integral type Hilbert operator Iμα+1(f)(z)=∫01f(t)(1−tz)α+1dμ(t)(α>−1).$$ {\mathcal{I}}_{\mu_{\alpha +1}}(f)(z)={\int}_0^1\frac{f(t)}{{\left(1- tz\right)}^{\alpha +1}} d\mu (t)\kern0.30em \left(\alpha >-1\right). $$The operator Iμ1$$ {\mathcal{I}}_{\mu_1} $$ has been extensively studied recently. The aim of this paper is to study the boundedness (resp. compactness) of Iμα+1$$ {\mathcal{I}}_{\mu_{\alpha +1}} $$ acting from the normal weight Bloch space into another of the same kind. As consequences of our study, we get completely results for the boundedness of Iμα+1$$ {\mathcal{I}}_{\mu_{\alpha +1}} $$ acting between Bloch type spaces, and between logarithmic Bloch spaces. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GENERALIZED integrals
*COMPOSITION operators
*COMPACT operators
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 46
- Issue :
- 17
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 173586056
- Full Text :
- https://doi.org/10.1002/mma.9572