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Two-sided estimates of the approximation numbers of certain Volterra integral operators

D. EdmundsW. EvansD. Harris — 1997

Studia Mathematica

We consider the Volterra integral operator T : L p ( + ) L p ( + ) defined by ( T f ) ( x ) = v ( x ) ʃ 0 x u ( t ) f ( t ) d t . Under suitable conditions on u and v, upper and lower estimates for the approximation numbers a n ( T ) of T are established when 1 < p < ∞. When p = 2 these yield l i m n n a n ( T ) = π - 1 ʃ 0 | u ( t ) v ( t ) | d t . We also provide upper and lower estimates for the α and weak α norms of (an(T)) when 1 < α < ∞.

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