Two methods for the inverse problem of memory reconstruction.
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Bukhgejm, A.L., Kalinina, N.I., Kardakov, V.B. (2000)
Siberian Mathematical Journal
Yves Rakotondratsimba (1998)
Publicacions Matemàtiques
New sufficient conditions on the weight functions u(.) and v(.) are given in order that the fractional maximal [resp. integral] operator Ms [resp. Is], 0 ≤ s < n, [resp. 0 < s < n] sends the weighted Lebesgue space Lp(v(x)dx) into Lp(u(x)dx), 1 < p < ∞. As a consequence a characterization for this estimate is obtained whenever the weight functions are radial monotone.
W. Evans, D. Harris, J. Lang (1998)
Studia Mathematica
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].
D. Edmunds, W. Evans, D. Harris (1997)
Studia Mathematica
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 < ∞.
Vakhtang Kokilashvili, Alexander Meskhi (2006)
Banach Center Publications
Necessary and sufficient conditions governing two-weight norm estimates for multiple Hardy and potential operators are presented. Two-weight inequalities for potentials defined on nonhomogeneous spaces are also discussed. Sketches of the proofs for most of the results are given.
Kokilashvili, V., Meskhi, A. (1999)
Georgian Mathematical Journal
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