期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:450
The index of weighted singular integral operators with shifts and slowly oscillating data
Article
Karlovich, Alexei Yu.1  Karlovich, Yuri I.2  Lebre, Amarino B.3 
[1] Univ Nova Lisboa, Fac Ciencias & Tecnol, Dept Matemat, Ctr Matemat & Aplicacoes, P-2829516 Caparica, Portugal
[2] Univ Autonoma Estado Morelos, Ctr Invest Ciencias, Inst Invest Ciencias Basicas & Aplicadas, Ave Univ 1001, Cuernavaca 62209, Morelos, Mexico
[3] Univ Lisbon, Inst Super Tecn, Dept Matemat, Ctr Anal Func Estruturas Lineares & Aplicacoes, Ave Rovisco Pais, P-1049001 Lisbon, Portugal
关键词: Orientation-preserving shift;    Weighted Cauchy singular integral operator;    Slowly oscillating function;    Semi-almost periodic function;    Fredhohnness;    Index;   
DOI  :  10.1016/j.jmaa.2017.01.052
来源: Elsevier
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【 摘 要 】

Let alpha and beta be orientation-preserving diffeomorphism (shifts) of R+ = (0, infinity) onto itself with the only fixed points 0 and infinity. We establish a Fredholm criterion and calculate the index of the weighted singular integral operator with shifts (aI - bUa)P-lambda(+) + (cI - dU(beta))P-gamma(-), acting on the space LP(IR+), where P-r(+/-) = (I +/- S-gamma)/2 are the operators associated to the weighted Cauchy singular integral operator S-gamma given by (S(gamma)f)(t) = 1/pi i integral(R+) (t/tau) f(tau)/ tau- t dr with gamma is an element of C satisfying 0 < 1/p+R gamma < 1, and U-alpha, U-beta are the isometric shift operators given by U(alpha)f = (alpha')(1/p) (f o alpha), U (beta)f - (beta')(1/p) (f o beta) under the assumptions that the coefficients a, b, c, d and the derivatives alpha',beta' of the shifts are bounded and continuous on R+ and. admit discontinuities of slowly oscillating type at 0 and infinity. (C) 2017 Elsevier Inc. All rights reserved.

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