March 2010 - Banach - mathdept.okstate.edu

Abstract of a paper by Tuomas Hyt\"onen and Mikko Kemppainen
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry" by Tuomas Hyt\"onen and Mikko Kemppainen. Abstract: Hyt\"onen, McIntosh and Portal (J. Funct. Anal., 2008) proved two vector-valued generalizations of the classical Carleson embedding theorem, both of them requiring the boundedness of a new vector-valued maximal operator, and the other one also the type p property of the underlying Banach space as an assumption. We show that these conditions are also necessary for the respective embedding theorems, thereby obtaining new equivalences between analytic and geometric properties of Banach spaces. Archive classification: math.FA Mathematics Subject Classification: 42B25 (Primary) 46E40 (Secondary) Remarks: 10 pages The source file(s), carleson.bbl: 2240 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.2876 or http://arXiv.org/abs/1002.2876 or by email in unzipped form by transmitting an empty message with subject line uget 1002.2876 or in gzipped form by using subject line get 1002.2876 to: math(a)arXiv.org.

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Abstract of a paper by Jan Vybiral
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "A variant of the Johnson-Lindenstrauss lemma for circulant matrices" by Jan Vybiral. Abstract: We continue our study of the Johnson-Lindenstrauss lemma and its connection to circulant matrices started in \cite{HV}. We reduce the bound on $k$ from $k=O(\varepsilon^{-2}\log^3n)$ proven there to $k=O(\varepsilon^{-2}\log^2n)$. Our technique differs essentially from the one used in \cite{HV}. We employ the discrete Fourier transform and singular value decomposition to deal with the dependency caused by the circulant structure. Archive classification: math.FA Mathematics Subject Classification: 52C99, 68Q01 The source file(s), Johnson_Lind2.tex: 21785 bytes, is(are) stored in gzipped form as 1002.2847.gz with size 8kb. The corresponding postcript file has gzipped size 84kb. Submitted from: jan.vybiral(a)oeaw.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.2847 or http://arXiv.org/abs/1002.2847 or by email in unzipped form by transmitting an empty message with subject line uget 1002.2847 or in gzipped form by using subject line get 1002.2847 to: math(a)arXiv.org.

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Abstract of a paper by Constantinos Kardaras and Gordan Zitkovic
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "Forward-convex convergence of sequences in $\mathbb{L}^0_+$" by Constantinos Kardaras and Gordan Zitkovic. Abstract: For a sequence in $\mathbb{L}^0_+$, we provide simple necessary and sufficient conditions to ensure that each sequence of its forward convex combinations converges to the same limit. These conditions correspond to a measure-free version of the notion of uniform integrability and are related to the numeraire problem of mathematical finance. Archive classification: math.FA math.PR Mathematics Subject Classification: 46A16; 46E30; 60A10 Remarks: 14 pages The source file(s), fcc.bbl: 3371 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.1889 or http://arXiv.org/abs/1002.1889 or by email in unzipped form by transmitting an empty message with subject line uget 1002.1889 or in gzipped form by using subject line get 1002.1889 to: math(a)arXiv.org.

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Abstract of a paper by Necip Simsek
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "On some geometric properties of sequence space defined by de la Vallee-Poussin mean" by Necip Simsek. Abstract: In this work, we investigate k-nearly uniform convex(k-NUC) and the uniform Opial properties of the sequence space defined by de la Vallee-Poussin mean. Also we give some corollaries concerning the geometrical properties of this space. Archive classification: math.FA Mathematics Subject Classification: 46A45, 46B20, 46B45 Remarks: 9 pages, no figure The source file(s), Manuscript-arXiv.tex: 29046 bytes, is(are) stored in gzipped form as 1002.1498.gz with size 8kb. The corresponding postcript file has gzipped size 84kb. Submitted from: nsimsek(a)adiyaman.edu.tr The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.1498 or http://arXiv.org/abs/1002.1498 or by email in unzipped form by transmitting an empty message with subject line uget 1002.1498 or in gzipped form by using subject line get 1002.1498 to: math(a)arXiv.org.

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Abstract of a paper by Simon Foucart, Alain Pajor, Holger Rauhut, and Tino Ullrich
by alspach＠fourier.math.okstate.edu 22 Mar '10

22 Mar '10

This is an announcement for the paper "The Gelfand widths of $\ell_p$-balls for $0<p\leq 1$" by Simon Foucart, Alain Pajor, Holger Rauhut, and Tino Ullrich. Abstract: We provide sharp lower and upper bounds for the Gelfand widths of $\ell_p$-balls in the $N$-dimensional $\ell_q^N$-space for $0<p\leq 1$ and $p<q \leq 2$. Such estimates are highly relevant to the novel theory of compressive sensing, and our proofs rely on methods from this area. Archive classification: math.FA cs.IT math.IT Mathematics Subject Classification: 41A46, 46B09 Remarks: 15 pages The source file(s), GelfandSAHTarxiv.tex: 45830 bytes, is(are) stored in gzipped form as 1002.0672.gz with size 15kb. The corresponding postcript file has gzipped size 84kb. Submitted from: tino.ullrich(a)hcm.uni-bonn.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1002.0672 or http://arXiv.org/abs/1002.0672 or by email in unzipped form by transmitting an empty message with subject line uget 1002.0672 or in gzipped form by using subject line get 1002.0672 to: math(a)arXiv.org.

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Conference "Banach Space Geometry"
by astashkn＠ssu.samara.ru 22 Mar '10

22 Mar '10

First Announcement for the conference "Banach Space Geometry", in honor of Evgeny Semenov's 70th birthday, to be held September 5--11, 2010 at the Euler International Mathematical Institute in Saint-Petersburg, Russia. We would like to announce that the website for the conference http://www.pdmi.ras.ru/EIMI/2010/bsg/1ann.html has been updated and now includes visa information and preliminary list of participants. Sincerely yours, Sergey Astashkin, Sergey Novikov

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Abstract of a paper by Aicke Hinrichs and Jan Vybiral
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "Johnson-Lindenstrauss lemma for circulant matrices" by Aicke Hinrichs and Jan Vybiral. Abstract: We prove a variant of a Johnson-Lindenstrauss lemma for matrices with circulant structure. This approach allows to minimise the randomness used, is easy to implement and provides good running times. The price to be paid is the higher dimension of the target space $k=O(\varepsilon^{-2}\log^3n)$ instead of the classical bound $k=O(\varepsilon^{-2}\log n)$. Archive classification: math.FA cs.IT math.IT Mathematics Subject Classification: 52C99; 68Q01 The source file(s), Hinrichs_Vybiral.tex: 18930 bytes, is(are) stored in gzipped form as 1001.4919.gz with size 7kb. The corresponding postcript file has gzipped size 84kb. Submitted from: jan.vybiral(a)oeaw.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.4919 or http://arXiv.org/abs/1001.4919 or by email in unzipped form by transmitting an empty message with subject line uget 1001.4919 or in gzipped form by using subject line get 1001.4919 to: math(a)arXiv.org.

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Abstract of a paper by Paul F.X. Mueller and Markus Passenbrunner
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "A representation theorem for singular integral operators on spaces of homogeneous type" by Paul F.X. Mueller and Markus Passenbrunner. Abstract: Let (X,d,\mu) be a space of homogeneous type and E a UMD Banach space. Under the assumption mu({x})=0 for all x in X, we prove a representation theorem for singular integral operators on (X,d,mu) as a series of simple shifts and rearrangements plus two paraproducts. This gives a T(1) Theorem in this setting. Archive classification: math.FA Mathematics Subject Classification: 42B20; 60G42; 46E40; 47B38 The source file(s), Basis.eps: 11807 bytes The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.4926 or http://arXiv.org/abs/1001.4926 or by email in unzipped form by transmitting an empty message with subject line uget 1001.4926 or in gzipped form by using subject line get 1001.4926 to: math(a)arXiv.org.

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Abstract of a paper by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "The McShane integral in weakly compactly generated spaces" by Antonio Aviles, Grzegorz Plebanek, and Jose Rodriguez. Abstract: Di Piazza and Preiss asked whether every Pettis integrable function defined on [0,1] and taking values in a weakly compactly generated Banach space is McShane integrable. In this paper we answer this question in the negative. Archive classification: math.FA math.PR Mathematics Subject Classification: 28B05; 46B10; 46B26 The source file(s), McShaneWCGFinal.tex: 53304 bytes, is(are) stored in gzipped form as 1001.4896.gz with size 16kb. The corresponding postcript file has gzipped size 84kb. Submitted from: avileslo(a)um.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.4896 or http://arXiv.org/abs/1001.4896 or by email in unzipped form by transmitting an empty message with subject line uget 1001.4896 or in gzipped form by using subject line get 1001.4896 to: math(a)arXiv.org.

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Abstract of a paper by David Cruz-Uribe, Jose Maria Martell, and Carlos Perez
by alspach＠fourier.math.okstate.edu 05 Mar '10

05 Mar '10

This is an announcement for the paper "Sharp weighted estimates for classical operators" by David Cruz-Uribe, Jose Maria Martell, and Carlos Perez. Abstract: We give a new proof of the sharp one weight $L^p$ inequality for any operator $T$ that can be approximated by Haar shift operators such as the Hilbert transform, any Riesz transform, the Beurling-Ahlfors operator. Our proof avoids the Bellman function technique and two weight norm inequalities. We use instead a recent result due to A. Lerner to estimate the oscillation of dyadic operators. Our method is flexible enough to prove the corresponding sharp one-weight norm inequalities for some operators of harmonic analysis: the maximal singular integrals associated to $T$, Dyadic square functions and paraproducts, and the vector-valued maximal operator of C. Fefferman-Stein. Also we can derive a very sharp two-weight bump type condition for $T$. Archive classification: math.CA math.FA Mathematics Subject Classification: 42B20; 42B25 The source file(s), dyadic-hilbert.tex: 72598 bytes, is(are) stored in gzipped form as 1001.4254.gz with size 21kb. The corresponding postcript file has gzipped size 84kb. Submitted from: carlosperez(a)us.es The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1001.4254 or http://arXiv.org/abs/1001.4254 or by email in unzipped form by transmitting an empty message with subject line uget 1001.4254 or in gzipped form by using subject line get 1001.4254 to: math(a)arXiv.org.

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