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

• Autorzy: W. D. Evans , D. J. Harris , J. Lang
• Języki publikacji: EN

Abstrakty

EN

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].

Kategorie tematyczne

• 47G10: Integral operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1998
• Tom: 130
• Numer: 2
• Strony: 171-192

Daty

wydano

1998

otrzymano

1997-09-01

poprawiono

1997-12-08

Twórcy

autor

W. D. Evans

• School of Mathematics, University of Wales, Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K.

autor

D. J. Harris

• School of Mathematics, University of Wales, Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K.

autor

J. Lang

• School of Mathematics, University of Wales, Cardiff, Senghennydd Road, Cardiff CF2 4YH, U.K.

Bibliografia

• [1] D. E. Edmunds and W. D. Evans, Spectral Theory and Differential Operators, Oxford Univ. Press, Oxford, 1987.
• [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.
• [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.
• [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.
• [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.
• [6] B. Opic and A. Kufner, Hardy-type Inequalities, Pitman Res. Notes Math. Ser. 219, Longman Sci. & Tech., Harlow, 1990.