New PDF release: Advanced Courses of Mathematical Analysis 2: Proceedings of

By Velasco M. V. (Ed), Rodriguez-Palacios A. (Ed)

ISBN-10: 0072345179

ISBN-13: 9780072345179

This quantity includes a set of articles by way of top researchers in mathematical research. It offers the reader with an in depth evaluation of recent instructions and advances in themes for present and destiny examine within the box.

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Extra resources for Advanced Courses of Mathematical Analysis 2: Proceedings of the 2nd International School Granada, Spain 20 - 24 September 2004

Example text

Xnl)-' so that the weak type (1,l) inequality cannot be satisfied. On the other hand, M s f (x) is always pointwise bounded by the composition M I (M2(. . (Mn f ) . . )) where the Mj are the directional operators defined in the previous section. Each one of these operators is bounded on Lp(R") so that M s is also bounded on LP (R") . As a corollary we can say that the differentiation holds for rectangles with sides parallel to the coordinate axes if f E LEc for some p > 1. This differentiation result had been proved in the 1930's by A.

Lotz) to extend a tensor norm a on FIN to a tensor norm on NORM (see Ref. [ 5 , Ch. II]), that was not considered by Grothendieck. And there is a good reason for that. In fact, if E and F have the approximation property, E @s F = E @= F , and it was 20 years after Grothendieck’s Rbume‘that the first space without the approximation property was discovered! Grothendieck considers some operations with the @-norms on FIN, which are extended to NORM by the finite hull procedure. In particular, when M , N E FIN, for every @-norm a , M @ N = (M’ ma N’)’ (algebraically).

Acad. Sci. Paris 231 (1950), 940-941. (4) Quelques rbultats sur les espaces wectoriels topologiques. C . R. Acad. Sci. Paris 233 (1951)’ 839-841. (5) Sur une notion de produit tensoriel topologique d’espaces wectoriels topologiques, et une classe remarquable d’espaces wectoriels like d cette notion. C . R. cad. ci. Paris 233 (1951), 1556-1558. 35 (6) Critkres de compacite' duns les espacies fonctionnels ge'ne'raux. Amer. J. of Math. 74 (1952), 168-186. (7) Sur les applications line'aires faiblement compactes d'espaces du type C(K).

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Advanced Courses of Mathematical Analysis 2: Proceedings of the 2nd International School Granada, Spain 20 - 24 September 2004 by Velasco M. V. (Ed), Rodriguez-Palacios A. (Ed)


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