On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

Alexei Yu Karlovich; Yuri I. Karlovich; Amarino B. Lebre

doi:10.1007/s11785-015-0452-0

On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

Alexei Yu Karlovich, Yuri I. Karlovich, Amarino B. Lebre

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

10 Citations (Scopus)

Abstract

Let be orientation-preserving diffeomorphism (shifts) of onto itself with the only fixed points and and be the isometric shift operators on given by , , and where then the operator is Fredholm on and its index is equal to zero. Moreover, its regularizers are described. the weighted Cauchy singular integral operator. We prove that if a , a and c, d are continuous on R + and slowly oscillating at 0 and8, and then the operator (I -cUa) P+ 2 +(I -dUa) P-2 is Fredholm on L p(R +) and its index is equal to zero. Moreover, its regularizers are described.

Original language	English
Pages (from-to)	1101-1131
Number of pages	31
Journal	Complex Analysis And Operator Theory
Volume	10
Issue number	6
DOIs	https://doi.org/10.1007/s11785-015-0452-0
Publication status	Published - Aug 2016

Keywords

Orientation-preserving shift
Weighted Cauchy singular integral operator
Slowly oscillating function
Fredholmness
Index
FREDHOLMNESS
ALGEBRA

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10.1007/s11785-015-0452-0

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@article{2a26dfbfb0d545ecaf07f8695022627a,

title = "On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data",

abstract = "Let be orientation-preserving diffeomorphism (shifts) of onto itself with the only fixed points and and be the isometric shift operators on given by , , and where then the operator is Fredholm on and its index is equal to zero. Moreover, its regularizers are described. the weighted Cauchy singular integral operator. We prove that if a , a and c, d are continuous on R + and slowly oscillating at 0 and8, and then the operator (I -cUa) P+ 2 +(I -dUa) P-2 is Fredholm on L p(R +) and its index is equal to zero. Moreover, its regularizers are described.",

keywords = "Orientation-preserving shift, Weighted Cauchy singular integral operator, Slowly oscillating function, Fredholmness, Index, FREDHOLMNESS, ALGEBRA",

author = "Karlovich, {Alexei Yu} and Karlovich, {Yuri I.} and Lebre, {Amarino B.}",

note = "This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects PEst-OE/MAT/UI0297/2014 (Centro de Matematica e Aplicacoes) and PEst-OE/MAT/UI4032 /2014 (Centro de Analise Funcional e Aplicacoes). The second author was also supported by the CONACYT Project No. 168104 (Mexico) and by PROMEP (Mexico) via {"}Proyecto de Redes{"}",

year = "2016",

month = aug,

doi = "10.1007/s11785-015-0452-0",

language = "English",

volume = "10",

pages = "1101--1131",

journal = "Complex Analysis And Operator Theory",

issn = "1661-8254",

publisher = "SPRINGER BASEL AG",

number = "6",

}

TY - JOUR

T1 - On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

AU - Karlovich, Alexei Yu

AU - Karlovich, Yuri I.

AU - Lebre, Amarino B.

N1 - This work was partially supported by the Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through the projects PEst-OE/MAT/UI0297/2014 (Centro de Matematica e Aplicacoes) and PEst-OE/MAT/UI4032 /2014 (Centro de Analise Funcional e Aplicacoes). The second author was also supported by the CONACYT Project No. 168104 (Mexico) and by PROMEP (Mexico) via "Proyecto de Redes"

PY - 2016/8

Y1 - 2016/8

N2 - Let be orientation-preserving diffeomorphism (shifts) of onto itself with the only fixed points and and be the isometric shift operators on given by , , and where then the operator is Fredholm on and its index is equal to zero. Moreover, its regularizers are described. the weighted Cauchy singular integral operator. We prove that if a , a and c, d are continuous on R + and slowly oscillating at 0 and8, and then the operator (I -cUa) P+ 2 +(I -dUa) P-2 is Fredholm on L p(R +) and its index is equal to zero. Moreover, its regularizers are described.

AB - Let be orientation-preserving diffeomorphism (shifts) of onto itself with the only fixed points and and be the isometric shift operators on given by , , and where then the operator is Fredholm on and its index is equal to zero. Moreover, its regularizers are described. the weighted Cauchy singular integral operator. We prove that if a , a and c, d are continuous on R + and slowly oscillating at 0 and8, and then the operator (I -cUa) P+ 2 +(I -dUa) P-2 is Fredholm on L p(R +) and its index is equal to zero. Moreover, its regularizers are described.

KW - Orientation-preserving shift

KW - Weighted Cauchy singular integral operator

KW - Slowly oscillating function

KW - Fredholmness

KW - Index

KW - FREDHOLMNESS

KW - ALGEBRA

U2 - 10.1007/s11785-015-0452-0

DO - 10.1007/s11785-015-0452-0

M3 - Article

SN - 1661-8254

VL - 10

SP - 1101

EP - 1131

JO - Complex Analysis And Operator Theory

JF - Complex Analysis And Operator Theory

IS - 6

ER -

On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

Abstract

Keywords

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