Two-sided estimates for the approximation numbers of Hardy-type operators in L and L¹
Evans, W. ; Harris, D. ; Lang, J.
Studia Mathematica, Tome 129 (1998), p. 171-192 / Harvested from The Polish Digital Mathematics Library

In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator T:Lp(+)Lp(+) defined by (Tf)(x)v(x)ʃ0u(t)f(t)dt when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].

Publié le : 1998-01-01
EUDML-ID : urn:eudml:doc:216550
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     author = {W. Evans and D. Harris and J. Lang},
     title = {Two-sided estimates for the approximation numbers of Hardy-type operators in $L^{$\infty$}$ and L$^1$},
     journal = {Studia Mathematica},
     volume = {129},
     year = {1998},
     pages = {171-192},
     zbl = {0912.47027},
     language = {en},
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Evans, W.; Harris, D.; Lang, J. Two-sided estimates for the approximation numbers of Hardy-type operators in $L^{∞}$ and L¹. Studia Mathematica, Tome 129 (1998) pp. 171-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv130i2p171bwm/

[00000] [1] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Oxford Univ. Press, Oxford, 1987. | Zbl 0628.47017

[00001] [2] D. E. Edmunds, W. D. Evans and D. J. Harris, Approximation numbers of certain Volterra integral operators, J. London Math. Soc. (2) 37 (1988), 471-489. | Zbl 0658.47049

[00002] [3] D. E. Edmunds, W. D. Evans and D. J. Harris, Two-sided estimates of the approximation numbers of certain Volterra integral operators, Studia Math. 124 (1997), 59-80. | Zbl 0897.47043

[00003] [4] D. E. Edmunds, P. Gurka and L. Pick, Compactness of Hardy-type integral operators in weighted Banach function spaces, ibid. 109 (1994), 73-90. | Zbl 0821.46036

[00004] [5] J. Newman and M. Solomyak, Two-sided estimates of singular values for a class of integral operators on the semi-axis, Integral Equations Operator Theory 20 (1994), 335-349. | Zbl 0817.47024

[00005] [6] B. Opic and A. Kufner, Hardy-type Inequalities, Pitman Res. Notes Math. Ser. 219, Longman Sci. & Tech., Harlow, 1990.