Spectral Theory of the Dirac Operator.
We consider the Volterra integral operator defined by . Under suitable conditions on u and v, upper and lower estimates for the approximation numbers of T are established when 1 < p < ∞. When p = 2 these yield . We also provide upper and lower estimates for the and weak norms of (an(T)) when 1 < α < ∞.
In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator defined by when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].
Sharp estimates are obtained for the rates of blow up of the norms of embeddings of Besov spaces in Lorentz spaces as the parameters approach critical values.
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