Download Advanced Courses of Mathematical Analysis II: Proceedings of by M. V. Velasco, A. Rodriguez-Palacios PDF

By M. V. Velasco, A. Rodriguez-Palacios

This quantity contains a set of articles through major researchers in mathematical research. It presents 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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Additional info for Advanced Courses of Mathematical Analysis II: Proceedings of the Second International School, Granada, Spain, 20 - 24 September 2004

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Ip (2) llP, is the norm in L P ( R ) . We observe the following. (i) For p = 00 the result is trivial: llMflloo 5 I l f l l m ; (ii) but for p = 1 the result is false: indeed, M f ( x ) 1z1-l when IC is large if f is not identically zero (integrability can fail even locally as was shown in ["I). : M f ( x )> A}l L C ,Ilflll forA > 0. ) It is good enough because 2 can be obtained for p > 1 from this estimate together with the trivial L" result (see the interpolation theorem below), and 3 is also good because Lebesgue's differentiation theorem comes as a corollary.

Amer. Math. ,No. 16, 1955. 9. A. Grothendieck, Rdsume' des resultats essentiels duns la the'orie des produits tensoriels topologiques et des espaces nucle'aires. Ann. Inst. Fourier Grenoble 4 (1952), 73-112 (appeared in 1954). 10. A. Grothendiek, Sur les applications line'aires faiblement compactes d'espaces du type C(K). Canadian J. , 5 (1953), 129-173. 11. A. Grothendieck, Re'sume' de la the'orie me'trique des produits tensoriels topologiques. Bol. Mat. Sao Paulo 8 (1953), 1-79 (appeared in 1956).

J. of Math. 74 (1952), 168-186. (7) Sur les applications line'aires faiblement compactes d'espaces du type C(K). Canadian J. Math. 5 (1953), 129-173. (8) Sur les espaces de solutions d'une classe ge'ne'rale d'e'quations aux de'rive'es partielles. J. Analyse Math. 2 (1953), 243-280. (9) Sur certains espaces de fonctions holomorphes, I. J. Reine Angew. Math. 192 (1953), 35-64. (10) Sur certains espaces de fonctions holomorphes, II. J. Reine Angew. Math. 192 (1953), 77-95. (11) Quelques points de la the'orie des produits tensoriels topologiques.

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