TY - JOUR

T1 - An algebra of integral operators with fixed singularities in kernels

AU - Duduchava, Roland

AU - Krupnik, Naum

AU - Shargorodsky, Eugene

N1 - Funding Information:
*Supported by EPSRC grant GR. / K01001

PY - 1999/4

Y1 - 1999/4

N2 - We continue the study of algebras generated by the Cauchy singular integral operator and integral operators with fixed singularities on the unit interval, started in R.Duduchava, E.Shargorodsky, 1990. Such algebras emerge when one considers singular integral operators with complex conjugation on curves with cusps. As one of possible applications of the obtained results we find an explicit formula for the local norms of the Cauchy singular integral operator on the Lebesgue space L2(Γ, ρ) , where Γ is a curve with cusps of arbitrary order and ρ is a power weight. For curves with angles and cusps of order 1 the formula was already known (see R.Avedanio, N.Krupnik, 1988 and R.Duduchava, N.Krupnik, 1995).

AB - We continue the study of algebras generated by the Cauchy singular integral operator and integral operators with fixed singularities on the unit interval, started in R.Duduchava, E.Shargorodsky, 1990. Such algebras emerge when one considers singular integral operators with complex conjugation on curves with cusps. As one of possible applications of the obtained results we find an explicit formula for the local norms of the Cauchy singular integral operator on the Lebesgue space L2(Γ, ρ) , where Γ is a curve with cusps of arbitrary order and ρ is a power weight. For curves with angles and cusps of order 1 the formula was already known (see R.Avedanio, N.Krupnik, 1988 and R.Duduchava, N.Krupnik, 1995).

UR - http://www.scopus.com/inward/record.url?scp=0040248895&partnerID=8YFLogxK

U2 - 10.1007/BF01291835

DO - 10.1007/BF01291835

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AN - SCOPUS:0040248895

SN - 0378-620X

VL - 33

SP - 406

EP - 425

JO - Integral Equations and Operator Theory

JF - Integral Equations and Operator Theory

IS - 4

ER -