Analysis at Urbana: Volume 2, Analysis in Abstract Spaces - download pdf or read online

By Earl R. Berkson, N. Tenney Peck, J. Jerry Uhl

ISBN-10: 052136437X

ISBN-13: 9780521364379

In the course of the educational 12 months 1986-7, the collage of Illinois was once host to a symposium on mathematical research which was once attended through a few of the top figures within the box. This publication arises out of this precise yr and lays emphasis at the synthesis of contemporary and classical research. The contributed articles through the members conceal the gamut of mainstream issues. This publication should be necessary to researchers in mathematical research.

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Extra info for Analysis at Urbana: Volume 2, Analysis in Abstract Spaces

Sample text

A constant depending only on and p The crucial fact behind Steckin's results is the boundedness of the Hilbert transform on for 1 < P < w. LP(~) , or its discrete analogue on The Banach spaces X such that the vector-valued LP(~,X) Hilbert transform is bounded on LP(Z) , 1 < P < w have recently for been characterized as those with the unconditionality property for martingale differences (written more briefly as precisely X e UMD X e UMD). by definition if and only if, for More 1 < P

2)). such projection-valued integrals (in the Cauchy Spectral decompositions in terms of functions were first discussed in a Banach space context by Smart and Ringrose [14,16]. 3) A = AdE(A) J for some compact interval operators. J in IR , calling them wel 1 - bounded Such operators on reflexive spaces may be characterized in terms of a functional calculus based on the Banach algebra of absolutely continuous functions on J . 3) is interpreted E(-) act on the dual space of in a weak-* sense after formal 30 Berkson & Gillespie: Spectral decompositions integration by parts.

M. Riesz, Sur les fonctions 27(1928), 218-244. 14. R. Ringrose, On well-bounded 1(1960), 334-343. operators, 16. R. Ringrose, On wel1-bounded Soc. (3), 13(1963), 613-638. operators 16. R. Smart, Conditionally convergent spectral Australian Math. , 1(1960), 319-333. 17. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton Math. Series, No. 32, Princeton Univ. , 1971. DEPARTMENT OF MATHEMATICS UNIVERSITY OF ILLINOIS 1409 W. GREEN ST. A. conjugu^es , Math. Zeitschrift, J.

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Analysis at Urbana: Volume 2, Analysis in Abstract Spaces by Earl R. Berkson, N. Tenney Peck, J. Jerry Uhl


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