Geodesic
On inequalities for integral operators
Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 126-133

Voir la notice de l'article provenant de la source Cambridge University Press

In two papers [3] and [4], the author has extended the inequality of Schur (Theorem 319 of [2]) to cases involving kernels which satisfy identities of the formThe purpose of this paper is to prove a general inequality, which includes the above and also the inequality of Young (Theorem 281 of [2]) as special cases. We shall give the results a general setting by considering functions defined on abstract measure spaces. From this we shall deduce an extension to n dimensions of the results given in [3], which also generalises a similar extension of the Schur inequality given by Stein and Weiss. In fact some cases of the other results given in [5] will follow directly from our theorem. 
Okikiolu, G. O. On inequalities for integral operators. Glasgow mathematical journal, Tome 11 (1970) no. 2, pp. 126-133. doi: 10.1017/S0017089500000975
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[1] 1.Cotlar, M. and Ortiz, E. L., On some inequalities for potential operators, Univ. Nac. La Plata Publ. Fac. Ci. Fisicomat. Serie Segunda Rev. 8 (1962), No. 1, 16–34. Google Scholar

[2] 2.Hardy, G. H., Littlewood, J. E. and Polya, G., Inequalities (Cambridge, 1934). Google Scholar

[3] 3.Okikiolu, G. O., Bounded linear transformations in Lp space, J. London Math. Soc, 41 (1966), 407–414. Google Scholar

[4] 4.Okikiolu, G. O., On certain bounded linear transformations in Lp′, Proc. London Math. Soc. (3) 17 (1967), 700–714. Google Scholar

[5] 5.Stein, E. M. and Weiss, G., Fractional integrals on n-dimensional Euclidean space, J. Math. Mech. 7 (1958), 503–514. Google Scholar

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