Norm estimates of the partial derivatives and Schwarz lemma for α-harmonic functions

Adel Khalfallah; Miodrag Mateljević

doi:10.1080/17476933.2023.2193742

Norm estimates of the partial derivatives and Schwarz lemma for α-harmonic functions

Adel Khalfallah^*, Miodrag Mateljević

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Suppose (Formula presented.) and (Formula presented.). Let (Formula presented.) be an α-harmonic mapping on (Formula presented.) with the boundary F being absolute continuous and (Formula presented.), where (Formula presented.). In this paper, we investigate the membership of (Formula presented.) and (Formula presented.) in the space (Formula presented.), the generalized Hardy space. We prove, if (Formula presented.), then both (Formula presented.) and (Formula presented.) are in (Formula presented.). If (Formula presented.), then (Formula presented.) and (Formula presented.) if and only if f is analytic. Finally, we investigate a Schwarz Lemma for α-harmonic functions.

Original language	English
Pages (from-to)	1182-1194
Number of pages	13
Journal	Complex Variables and Elliptic Equations
Volume	69
Issue number	7
DOIs	https://doi.org/10.1080/17476933.2023.2193742
State	Published - 2024

Bibliographical note

Publisher Copyright:
© 2023 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

Poisson integral
bergman space
hardy space
α-harmonic mapping

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1080/17476933.2023.2193742

Cite this

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title = "Norm estimates of the partial derivatives and Schwarz lemma for α-harmonic functions",

abstract = "Suppose (Formula presented.) and (Formula presented.). Let (Formula presented.) be an α-harmonic mapping on (Formula presented.) with the boundary F being absolute continuous and (Formula presented.), where (Formula presented.). In this paper, we investigate the membership of (Formula presented.) and (Formula presented.) in the space (Formula presented.), the generalized Hardy space. We prove, if (Formula presented.), then both (Formula presented.) and (Formula presented.) are in (Formula presented.). If (Formula presented.), then (Formula presented.) and (Formula presented.) if and only if f is analytic. Finally, we investigate a Schwarz Lemma for α-harmonic functions.",

keywords = "Poisson integral, bergman space, hardy space, α-harmonic mapping",

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doi = "10.1080/17476933.2023.2193742",

language = "English",

volume = "69",

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T1 - Norm estimates of the partial derivatives and Schwarz lemma for α-harmonic functions

AU - Khalfallah, Adel

AU - Mateljević, Miodrag

PY - 2024

Y1 - 2024

N2 - Suppose (Formula presented.) and (Formula presented.). Let (Formula presented.) be an α-harmonic mapping on (Formula presented.) with the boundary F being absolute continuous and (Formula presented.), where (Formula presented.). In this paper, we investigate the membership of (Formula presented.) and (Formula presented.) in the space (Formula presented.), the generalized Hardy space. We prove, if (Formula presented.), then both (Formula presented.) and (Formula presented.) are in (Formula presented.). If (Formula presented.), then (Formula presented.) and (Formula presented.) if and only if f is analytic. Finally, we investigate a Schwarz Lemma for α-harmonic functions.

AB - Suppose (Formula presented.) and (Formula presented.). Let (Formula presented.) be an α-harmonic mapping on (Formula presented.) with the boundary F being absolute continuous and (Formula presented.), where (Formula presented.). In this paper, we investigate the membership of (Formula presented.) and (Formula presented.) in the space (Formula presented.), the generalized Hardy space. We prove, if (Formula presented.), then both (Formula presented.) and (Formula presented.) are in (Formula presented.). If (Formula presented.), then (Formula presented.) and (Formula presented.) if and only if f is analytic. Finally, we investigate a Schwarz Lemma for α-harmonic functions.

KW - Poisson integral

KW - bergman space

KW - hardy space

KW - α-harmonic mapping

UR - https://www.scopus.com/pages/publications/85150743976

U2 - 10.1080/17476933.2023.2193742

DO - 10.1080/17476933.2023.2193742

M3 - Article

AN - SCOPUS:85150743976

SN - 1747-6933

VL - 69

SP - 1182

EP - 1194

JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 7

ER -

Norm estimates of the partial derivatives and Schwarz lemma for α-harmonic functions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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