The Plemelj–Privalov theorem in polyanalytic function theory

Lianet De la Cruz Toranzo; Ricardo Abreu Blaya; Juan Bory Reyes

doi:10.1016/j.jmaa.2018.03.023

The Plemelj–Privalov theorem in polyanalytic function theory

Lianet De la Cruz Toranzo, Ricardo Abreu Blaya, Juan Bory Reyes

Escuela Superior de Ingeniería Mecánica y Eléctrica (ESIME), Unidad Zacatenco

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

8 Scopus citations

Abstract

In this paper we prove that the higher order Lipschitz classes behave invariant under the action of a singular integral operator naturally arising in polyanalytic function theory. This result provides a generalization of the well-known theorem by Joseph Plemelj [16] and Ivan Privalov [17].

Original language	English
Pages (from-to)	517-533
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	463
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2018.03.023
State	Published - 15 Jul 2018

Keywords

Lipschitz classes
Polyanalytic functions
Singular integral operator

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10.1016/j.jmaa.2018.03.023

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title = "The Plemelj–Privalov theorem in polyanalytic function theory",

abstract = "In this paper we prove that the higher order Lipschitz classes behave invariant under the action of a singular integral operator naturally arising in polyanalytic function theory. This result provides a generalization of the well-known theorem by Joseph Plemelj [16] and Ivan Privalov [17].",

keywords = "Lipschitz classes, Polyanalytic functions, Singular integral operator",

author = "{De la Cruz Toranzo}, Lianet and {Abreu Blaya}, Ricardo and {Bory Reyes}, Juan",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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doi = "10.1016/j.jmaa.2018.03.023",

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T1 - The Plemelj–Privalov theorem in polyanalytic function theory

AU - De la Cruz Toranzo, Lianet

AU - Abreu Blaya, Ricardo

AU - Bory Reyes, Juan

PY - 2018/7/15

Y1 - 2018/7/15

N2 - In this paper we prove that the higher order Lipschitz classes behave invariant under the action of a singular integral operator naturally arising in polyanalytic function theory. This result provides a generalization of the well-known theorem by Joseph Plemelj [16] and Ivan Privalov [17].

AB - In this paper we prove that the higher order Lipschitz classes behave invariant under the action of a singular integral operator naturally arising in polyanalytic function theory. This result provides a generalization of the well-known theorem by Joseph Plemelj [16] and Ivan Privalov [17].

KW - Lipschitz classes

KW - Polyanalytic functions

KW - Singular integral operator

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U2 - 10.1016/j.jmaa.2018.03.023

DO - 10.1016/j.jmaa.2018.03.023

M3 - Artículo

SN - 0022-247X

VL - 463

SP - 517

EP - 533

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

The Plemelj–Privalov theorem in polyanalytic function theory

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Keywords

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