Characterizations of Bloch-Type Spaces of Harmonic Mappings

Joint Authors

Colonna, Flavia
Aljuaid, Munirah

Source

Journal of Function Spaces

Issue

Vol. 2019, Issue 2019 (31 Dec. 2019), pp.1-11, 11 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2019-08-05

Country of Publication

Egypt

No. of Pages

11

Main Subjects

Mathematics

Abstract EN

We study the Banach space BHα (α>0) of the harmonic mappings h on the open unit disk D satisfying the condition supz∈D(1-z2)α(hzz+hz¯z)<∞, where hz and hz¯ denote the first complex partial derivatives of h.

We show that several properties that are valid for the space of analytic functions known as the α-Bloch space extend to BHα.

In particular, we prove that for α>0 the mappings in BHα can be characterized in terms of a Lipschitz condition relative to the metric defined by dH,α(z,w)=sup{hz-hw:h∈BHα,hBHα≤1}.

When α>1, the harmonic α-Bloch space can be viewed as the harmonic growth space of order α-1, while for 0<α<1, BHα is the space of harmonic mappings that are Lipschitz of order 1-α.

American Psychological Association (APA)

Aljuaid, Munirah& Colonna, Flavia. 2019. Characterizations of Bloch-Type Spaces of Harmonic Mappings. Journal of Function Spaces،Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1174796

Modern Language Association (MLA)

Aljuaid, Munirah& Colonna, Flavia. Characterizations of Bloch-Type Spaces of Harmonic Mappings. Journal of Function Spaces No. 2019 (2019), pp.1-11.
https://search.emarefa.net/detail/BIM-1174796

American Medical Association (AMA)

Aljuaid, Munirah& Colonna, Flavia. Characterizations of Bloch-Type Spaces of Harmonic Mappings. Journal of Function Spaces. 2019. Vol. 2019, no. 2019, pp.1-11.
https://search.emarefa.net/detail/BIM-1174796

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-1174796