Hölder continuity of hyperbolic Poisson integral and hyperbolic Green integral

Lihua, Ma

doi:10.1007/s00605-022-01748-4

Monatsh Math

2022

DOI: 10.1007/s00605-022-01748-4

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Hölder continuity of hyperbolic Poisson integral and hyperbolic Green integral

Ma Lihua

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2023

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Cited by 3 publications

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On the behavior of Orlicz–Sobolev mappings with branching on the unit sphere

Mateljević

Sevost’yanov

2023

J Math Sci

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We study the mappings of the Orlicz-Sobolev classes with a branching defined in the unit ball of the Euclidean space. We have obtained estimates for the distortion of the distance under these mappings at the points of the unit sphere. Under some conditions, we have also obtained the Hölder continuity of the mappings mentioned above. If we suppose that the considered mappings are solutions to certain Laplacian-gradient inequalities, we get the Lipschitz property. In section 7-9, we review some results, prove a new result, Theorem 7.1, and outline the proof of Theorem 9.2.

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On the behavior of Orlicz–Sobolev mappings with branching on the unit sphere

Mateljević

Sevost’yanov

2023

J Math Sci

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Modulus of continuity of normal derivative of a harmonic functions at a boundary point

Arsenovic,

Mateljevic

2023

Filomat

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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) ? C?(y)/y for every x in E ? Rn, where ? is a majorant. The conditions are expressed in terms of behaviour of the Riesz transforms Rjf of f near points in E. We briefly investigate related questions for the cases of harmonic and hyperbolic harmonic functions in the unit ball.

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On the behavior of Orlicz-Sobolev mappings with branching on the unit sphere

Mateljević

Sevost’yanov

2023

UMB

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We study the mappings of the Orlicz--Sobolev classes with a branching defined in the unit ball of the Euclidean space. We have obtained estimates for the distortion of the distance under these mappings at the points of the unit sphere. Under some conditions, we have also obtained the Hölder continuity of the mappings mentioned above. If we suppose that the considered mappings are solutions to certain Laplacian-gradient inequalities, we get the Lipschitz property. In section 7-9, we review some results, prove a new result, Theorem 7.1, and outline the proof of Theorem 9.2.

show abstract

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Hölder continuity of hyperbolic Poisson integral and hyperbolic Green integral

Cited by 3 publications

References 13 publications

On the behavior of Orlicz–Sobolev mappings with branching on the unit sphere

On the behavior of Orlicz–Sobolev mappings with branching on the unit sphere

Modulus of continuity of normal derivative of a harmonic functions at a boundary point

On the behavior of Orlicz-Sobolev mappings with branching on the unit sphere

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