References
Bloom, S., Kerman, R.: Weighted norm inequalities for operators of Hardy type. Proc. Am. Math. Soc.113, 135–141 (1991)
Canavati, J.A., Galaz-Fontes, F.: Compactness of imbeddings between Banach spaces and applications to Sobolev spaces. J. Lond. Math. Soc., II. Ser.41, 511–525 (1990)
Carl, B.: Inequalities of Bernstein-Jackson type and the degree of compactness of operators in Banach spaces. Ann. Inst. Fourier35, 79–118 (1985)
Edmunds, D.E., Evans, W.D.: Spectral theory and differential operators. Oxford: Oxford University Press 1987
Edmunds, D.E., Evans, W.D., Harris, D.J.: Approximation numbers of certain Volterra integral operators. J. Lond. Math. Soc., II. Ser.37, 471–489 (1988)
Evans, W.D., Harris, D.J.: Sobolev embeddings for generalized ridged domains. Proc. Lond. Math. Soc., III. Ser.54, 141–175 (1987)
Juberg, R.K.: Measure of non-compactness and interpolation of compactness for a class of integral transformations. Duke Math. J.41, 511–525 (1974)
König, H.: Eigenvalue distribution of compact operators. Basel Boston Stuttgart: Birkhäuser 1986
Muckenhaupt, B.: Hardy inequalities with weights. Stud. Math.44, 31–38 (1972)
Mynbaev, K.T., Otelbaev, M.O.: Weighted function spaces and the spectrum of differential operators (Russian) Moscow: Nauka 1988
Oinarov, R.: Weighted inequalities for a class of integral operators. Sov. Math., Dokl.44, 291–293 (1992)
Pietsch, A.: Operator ideals, (VEB Deutscher Verlag Wiss., Berlin, 1978).
Stepanov, V.D.: Weighted inequalities for a class of Volterra convolution operators. J. Lond. Math. Soc., II. Ser.45, 232–242 (1992)
Stepanov, V.D.: Weighted norm inequalities of Hardy type for a class of integral operators. Preprint, Institute for Applied Math., Far-Eastern Branch Russian Acad. Sci., Khabarovsk, 1992
Stuart, C.A.: The measure of non-compactness of some linear integral operators. Proc. R. Soc. Edinb., Sect. A71, 167–179 (1973)
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The second author's research was partially supported by SERC, Grant GR/H53419
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Edmunds, D.E., Stepanov, V.D. The measure of non-compactness and approximation numbers of certain Volterra integral operators. Math. Ann. 298, 41–66 (1994). https://doi.org/10.1007/BF01459724
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DOI: https://doi.org/10.1007/BF01459724