Compactness of Commutators Arising in the Fredholm Theory of Singular Integral Operators with Shifts

Karlovich, Yuri I.

doi:10.1007/978-94-017-0227-0_9

Factorization, Singular Operators and Related Problems 2003

DOI: 10.1007/978-94-017-0227-0_9

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Compactness of Commutators Arising in the Fredholm Theory of Singular Integral Operators with Shifts

Yuri I. Karlovich

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Cited by 2 publications

References 15 publications

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On Mellin pseudodifferential operators with quasicontinuous symbols

Karlovich

2020

Math Methods in App Sciences

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Let QC(R + ) be the C * -algebra of quasicontinuous functions on R + = (0, ∞) and S R + be the Cauchy singular integral operator, and let p ∈ (1, ∞). The paper is devoted to studying Mellin pseudodifferential operators with quasicontinuous V(R)-valued symbols on Lebesgue spaces L p (R + , d ), where V(R) is the Banach algebra of absolutely continuous functions of bounded total variation on the real line R, and d (r) = dr/r. Applying obtained results on Mellin pseudodifferential operators with quasicontinuous V(R)-valued symbols, we study a Banach algebra p of modified singular integral operators on the space L p (R + ), which is generated by the operators of the form

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On Mellin pseudodifferential operators with quasicontinuous symbols

Karlovich

2020

Math Methods in App Sciences

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Sufficient Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

Karlovich

Lebre

2011

Integr. Equ. Oper. Theory

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Suppose α is an orientation preserving diffeomorphism (shift) of R+ = (0, ∞) onto itself with the only fixed points 0 and ∞. We establish sufficient conditions for the Fredholmness of the singular integral operator with shift (aI − bWα)P+ + (cI − dWα)P− acting on L p (R+) with 1 < p < ∞, where P± = (I ± S)/2, S is the Cauchy singular integral operator, and Wαf = f • α is the shift operator, under the assumptions that the coefficients a, b, c, d and the derivative α of the shift are bounded and continuous on R+ and may admit discontinuities of slowly oscillating type at 0 and ∞. Mathematics Subject Classification (2010). Primary 45E05; Secondary 47A53, 47B35, 47G10, 47G30.

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Compactness of Commutators Arising in the Fredholm Theory of Singular Integral Operators with Shifts

Cited by 2 publications

References 15 publications

On Mellin pseudodifferential operators with quasicontinuous symbols

On Mellin pseudodifferential operators with quasicontinuous symbols

Sufficient Conditions for Fredholmness of Singular Integral Operators with Shifts and Slowly Oscillating Data

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