# Two-sided estimates for the approximation numbers of Hardy-type operators in ${L}^{\infty}$ and L¹

Studia Mathematica (1998)

- Volume: 130, Issue: 2, page 171-192
- ISSN: 0039-3223

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topEvans, W., Harris, D., and Lang, J.. "Two-sided estimates for the approximation numbers of Hardy-type operators in $L^{∞}$ and L¹." Studia Mathematica 130.2 (1998): 171-192. <http://eudml.org/doc/216550>.

@article{Evans1998,

abstract = {In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator $T: L^p(ℝ^+) → L^p(ℝ^+)$ defined by $(Tf)(x) ≔ v(x) ʃ_\{0\}^\{∞\} u(t)f(t)dt$ when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].},

author = {Evans, W., Harris, D., Lang, J.},

journal = {Studia Mathematica},

keywords = {upper and lower estimates; asymptotic results; approximation numbers},

language = {eng},

number = {2},

pages = {171-192},

title = {Two-sided estimates for the approximation numbers of Hardy-type operators in $L^\{∞\}$ and L¹},

url = {http://eudml.org/doc/216550},

volume = {130},

year = {1998},

}

TY - JOUR

AU - Evans, W.

AU - Harris, D.

AU - Lang, J.

TI - Two-sided estimates for the approximation numbers of Hardy-type operators in $L^{∞}$ and L¹

JO - Studia Mathematica

PY - 1998

VL - 130

IS - 2

SP - 171

EP - 192

AB - In [2] and [3] upper and lower estimates and asymptotic results were obtained for the approximation numbers of the operator $T: L^p(ℝ^+) → L^p(ℝ^+)$ defined by $(Tf)(x) ≔ v(x) ʃ_{0}^{∞} u(t)f(t)dt$ when 1 < p < ∞. Analogous results are given in this paper for the cases p = 1,∞ not included in [2] and [3].

LA - eng

KW - upper and lower estimates; asymptotic results; approximation numbers

UR - http://eudml.org/doc/216550

ER -

## References

top- [1] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Oxford Univ. Press, Oxford, 1987. Zbl0628.47017
- [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. Zbl0658.47049
- [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. Zbl0897.47043
- [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. Zbl0821.46036
- [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. Zbl0817.47024
- [6] B. Opic and A. Kufner, Hardy-type Inequalities, Pitman Res. Notes Math. Ser. 219, Longman Sci. & Tech., Harlow, 1990.

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