Geodesic
Integral mean estimates for univalent and locally univalent harmonic mappings
Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 655-669

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DOI

We verify a long-standing conjecture on the membership of univalent harmonic mappings in the Hardy space, whenever the functions have a “nice” analytic part. We also produce a coefficient estimate for these functions, which is in a sense best possible. The problem is then explored in a new direction, without the additional hypothesis. Interestingly, our ideas extend to certain classes of locally univalent harmonic mappings. Finally, we prove a Baernstein-type extremal result for the function $\log (h'+cg')$, when $f=h+\overline {g}$ is a close-to-convex harmonic function, and c is a constant. This leads to a sharp coefficient inequality for these functions.
DOI : 10.4153/S0008439524000067
Mots-clés : Integral means, univalent harmonic functions, growth problems, Hardy space, Baernstein-type inequalities 
Das, Suman; Kaliraj, Anbareeswaran Sairam. Integral mean estimates for univalent and locally univalent harmonic mappings. Canadian mathematical bulletin, Tome 67 (2024) no. 3, pp. 655-669. doi: 10.4153/S0008439524000067
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     title = {Integral mean estimates for univalent and locally univalent harmonic mappings},
     journal = {Canadian mathematical bulletin},
     pages = {655--669},
     year = {2024},
     volume = {67},
     number = {3},
     doi = {10.4153/S0008439524000067},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439524000067/}
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