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
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
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 -