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Two weight norm inequality for the fractional maximal operator and the fractional integral operator.

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.

Two-sided estimates for the approximation numbers of Hardy-type operators in and L¹

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].

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

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 < ∞.

Two-weighted criteria for integral transforms with multiple kernels

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.

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