Geodesic
Modulus of continuity of normal derivative of a harmonic functions at a boundary point
Filomat, Tome 37 (2023) no. 25, p. 8667

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DOI

We give sufficient conditions which ensure that harmonic extension u = P[ f ] to the upper half space {(x, y) | x ∈ Rn, y > 0} of a function f ∈ Lp(Rn) satisfies estimate ∂u ∂y (x, y) ≤ Cω(y)/y for every x in E ⊂ Rn, where ω is a majorant. The conditions are expressed in terms of behaviour of the Riesz transforms Rj f of f near points in E. We briefly investigate related questions for the cases of harmonic and hyperbolic harmonic functions in the unit ball.
DOI : 10.2298/FIL2325667A
Classification : 42B15, 42B30
Keywords: Poisson kernel, Harmonic functions, Modulus of conitinuity 
Miloš Arsenović; Miodrag Mateljević. Modulus of continuity of normal derivative of a harmonic functions at a boundary point. Filomat, Tome 37 (2023) no. 25, p. 8667 . doi: 10.2298/FIL2325667A
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     title = {Modulus of continuity of normal derivative of a harmonic functions at a boundary point},
     journal = {Filomat},
     pages = {8667 },
     year = {2023},
     volume = {37},
     number = {25},
     doi = {10.2298/FIL2325667A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2325667A/}
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