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 -