Bohr radius for locally univalent harmonic mappings | Zendy

Kayumov Ilgiz R | Zendy; Ponnusamy Saminathan | Zendy; Shakirov Nail | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Premium

Bohr radius for locally univalent harmonic mappings

Author(s) -

Kayumov Ilgiz R,

Ponnusamy Saminathan,

Shakirov Nail

Publication year - 2018

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201700068

Subject(s) - bohr radius , bohr model , mathematics , bounded function , infimum and supremum , radius , unit disk , harmonic , mathematical analysis , space (punctuation) , harmonic function , harmonic oscillator , pure mathematics , quantum mechanics , physics , computer security , computer science , quantum dot , linguistics , philosophy

We consider the class of all sense‐preserving harmonic mappings f = h + g ¯of the unit disk D , where h and g are analytic with g ( 0 ) = 0 , and determine the Bohr radius if any one of the following conditions holds: 1. h is bounded in D . 2. h satisfies the conditionReh ( z ) ≤ 1 in D with h ( 0 ) > 0 . 3. both h and g are bounded in D . 4. h is bounded andg ′ ( 0 ) = 0 . We also consider the problem of determining the Bohr radius when the supremum of the modulus of the dilatation of f in D is strictly less than 1. In addition, we determine the Bohr radius for the space B of analytic Bloch functions and the space B H of harmonic Bloch functions. The paper concludes with two conjectures.

This content is not available in your region!

Continue researching here.

Having issues? You can contact us here

Accelerating Research