Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference5 articles.
1. On Certain Bounded Linear Transformations in Lp
2. Bounded Linear Transformations in Lp
Space
3. On some inequalities for potential operators;Cotlar;Univ. Nac. La Plata Publ. Fac. Ci. Fisicomat. Serie Segunda Rev.,1962
4. Fractional integrals on n-dimensional Euclidean space;Stein;J. Math. Mech.,1958
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