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

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

This quantity contains a set of articles through top researchers in mathematical research. It offers the reader with an in depth evaluation of recent instructions and advances in issues for present and destiny study within the box.

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Extra info for Advanced Courses of Mathematical Analysis II: Proceedings of the Second International School, Granada, Spain, 20 - 24 September 2004

Example text

1. The Hardy-Littlewood maximal operator i s of weak type ( 1 , l ) and of strong type ( p , p ) f o r 1 < p < 00. There are several proofs of the this theorem. The original paper by Hardy and Littlewood proves the strong type by using a limiting argument from the analogous theorem for finite sums and decreasing rearrangements. Shortly after (1931) R. M. Gabriel published a simpler proof that inspired a beautiful proof of F. h e s z (1932) in which he used his “rising sun lemma” to obtain the weak inequality.

Then for each Hilbert space H , sup { 34 This is why the theorem is now called Grothendieck’s inequality. Their proof owes much to that of Grothendieck, but this formulation, allied with the theory of p-summing operators, avoids much of the machinery of tensor products to present many of Grothendieck’s ideas. Just in Ref. ) are obtained. (See Ref. [ 7, Chapter 31 for a modern exposition). As in the case of his Thesis, Grothendieck published some of the results of the Rksume‘before its appearance (Refs.

As we have said, Grothendieck left the IHES in 1970. After that, he became vividly interested in Ecology for some time, and founded the group Survivre et Vivre. For two years, he had a temporary post a t the prestigious Colle'ge de France in Paris, but he used his lectures to talk more about questions of ecology and peace than of mathematics. In 1972 Grothendieck obtained French citizenship and lectured at Montpellier University from 1973 to 1984. In 1984 he applied for a position of Director or Research a t CNRS, but specified that he did not want any regular research duty.

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