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 | |
【 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.
【 授权许可】
Free
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
10_1016_j_jmaa_2017_01_052.pdf | 563KB | download |