TY - CHAP

T1 - Semi-Fredholmness of Weighted Singular Integral Operators with Shifts and Slowly Oscillating Data

AU - Karlovich, Alexei Yu

AU - Karlovich, Yuri I.

AU - Lebre, Amarino B.

N1 - info:eu-repo/grantAgreement/FCT/5876/147204/PT#
info:eu-repo/grantAgreement/FCT/5876/147208/PT#
Sem pdf conforme despacho.
The second author was also supported by the SEP-CONACYT Project No. 168104 (México).

PY - 2018

Y1 - 2018

N2 - Let α, β be orientation-preserving homeomorphisms of [0,∞] onto itself, which have only two fixed points at 0 and ∞, and whose restrictions to ℝ+ = (0,∞) are diffeomorphisms, and let Uα, Uβ be the corresponding isometric shift operators on the space Lp(ℝ+) given by (Formula presented) for (Formula presented). We prove sufficient conditions for the right and left Fredholmness on Lp(ℝ+) of singular integral operators of the form (Formula presented), where (Formula presented) is a weighted Cauchy singular integral operator, (Formula presented) and (Formula presented) are operators in the Wiener algebras of functional operators with shifts. We assume that the coefficients ak, bk for (Formula presented) and the derivatives of the shifts (Formula presented) are bounded continuous functions on ℝ+ which may have slowly oscillating discontinuities at 0 and ∞.

AB - Let α, β be orientation-preserving homeomorphisms of [0,∞] onto itself, which have only two fixed points at 0 and ∞, and whose restrictions to ℝ+ = (0,∞) are diffeomorphisms, and let Uα, Uβ be the corresponding isometric shift operators on the space Lp(ℝ+) given by (Formula presented) for (Formula presented). We prove sufficient conditions for the right and left Fredholmness on Lp(ℝ+) of singular integral operators of the form (Formula presented), where (Formula presented) is a weighted Cauchy singular integral operator, (Formula presented) and (Formula presented) are operators in the Wiener algebras of functional operators with shifts. We assume that the coefficients ak, bk for (Formula presented) and the derivatives of the shifts (Formula presented) are bounded continuous functions on ℝ+ which may have slowly oscillating discontinuities at 0 and ∞.

KW - Left Fredholmness

KW - Mellin pseudodifferential operator

KW - Right Fredholmness

KW - Slowly oscillating shift

KW - Weighted singular integral operator

KW - Wiener algebra of functional operators

UR - http://www.scopus.com/inward/record.url?scp=85052383563&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-72449-2_11

DO - 10.1007/978-3-319-72449-2_11

M3 - Chapter

AN - SCOPUS:85052383563

VL - 267

T3 - Operator Theory: Advances and Applications

SP - 221

EP - 246

BT - Operator Theory

PB - Springer International Publishing

ER -