A note on the Fredholm theory of singular integral operators with Cauchy and Mellin kernels
A result on the necessity and sufficiency of conditions for the Fredholmness of singular integral operators in weighted Lp -spaces on the interval (0, 1) of the real axis ℝ is proved together with a respective Fredholm index formula. These operators are composed by the Cauchy singular integral operator, Mellin operators and operators of multiplication by piecewise continuous functions.
KeywordsSingular integral operators Cauchy kernel Mellin kernel Fredholm theory
Mathematics Subject Classification (2010)Primary 45E05 Secondary 45E10
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