June 2012 - Banach - mathdept.okstate.edu

Abstract of a paper by David Alonso-Gutierrez and Joscha Prochno Title: Estimating support functions of random polytopes via Orlicz norms
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "Estimating support functions of random polytopes via Orlicz norms" by David Alonso-Gutierrez and Joscha Prochno. Abstract: We study the expected value of support functions of random polytopes in a certain direction, where the random polytope is given by independent random vectors uniformly distributed in an isotropic convex body. All results are obtained by an utterly novel approach, using probabilistic estimates in connection with Orlicz norms that were not used in this connection before. Archive classification: math.FA Mathematics Subject Classification: Primary 52A22, Secondary 52A23, 05D40, 46B09 Submitted from: prochno(a)math.uni-kiel.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1205.2023 or http://arXiv.org/abs/1205.2023

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Abstract of a paper by Tuomas P. Hytonen and Michael T. Lacey
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "Pointwise convergence of vector-valued Fourier series" by Tuomas P. Hytonen and Michael T. Lacey. Abstract: We prove a vector-valued version of Carleson's theorem: Let Y=[X,H]_t be a complex interpolation space between a UMD space X and a Hilbert space H. For p\in(1,\infty) and f\in L^p(T;Y), the partial sums of the Fourier series of f converge to f pointwise almost everywhere. Apparently, all known examples of UMD spaces are of this intermediate form Y=[X,H]_t. In particular, we answer affirmatively a question of Rubio de Francia on the pointwise convergence of Fourier series of Schatten class valued functions. Archive classification: math.FA math.CA Mathematics Subject Classification: 42B20, 42B25 Remarks: 26 pages Submitted from: tuomas.hytonen(a)helsinki.fi The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1205.0261 or http://arXiv.org/abs/1205.0261

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Abstract of a paper by Szymon Glab, Pedro L. Kaufmann and Leonardo Pellegrini
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "Spaceability and algebrability of sets of nowhere integrable functions" by Szymon Glab, Pedro L. Kaufmann and Leonardo Pellegrini. Abstract: We show that the set of Lebesgue integrable functions in $[0,1]$ which are nowhere essentially bounded is spaceable, improving a result from [F. J. Garc\'{i}a-Pacheco, M. Mart\'{i}n, and J. B. Seoane-Sep\'ulveda. \textit{Lineability, spaceability, and algebrability of certain subsets of function spaces,} Taiwanese J. Math., \textbf{13} (2009), no. 4, 1257--1269], and that it is strongly $\mathfrak{c}$-algebrable. We prove strong $\mathfrak{c}$-algebrability and non-separable spaceability of the set of functions of bounded variation which have a dense set of jump discontinuities. Applications to sets of Lebesgue-nowhere-Riemann integrable and Riemann-nowhere-Newton integrable functions are presented as corollaries. In addition we prove that the set of Kurzweil integrable functions which are not Lebesgue integrable is spaceable (in the Alexievicz norm) but not $1$-algebrable. We also show that there exists an infinite dimensional vector space $S$ of differentiable functions such that each element of the $C([0,1])$-closure of $S$ is a primitive to a Kurzweil integrable function, in connection to a classic spaceability result from [V. I. Gurariy, \textit{Subspaces and bases in spaces of continuous functions (Russian),} Dokl. Akad. Nauk SSSR, \textbf{167} (1966), 971--973]. Archive classification: math.FA Remarks: accepted on 2011 Submitted from: leoime(a)yahoo.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.6404 or http://arXiv.org/abs/1204.6404

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Abstract of a paper by Joscha Prochno
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "The embedding of 2-concave Musielak-Orlicz spaces into L_1 via l_2-matrix-averages" by Joscha Prochno. Abstract: In this note we prove that $\frac{1}{n!} \sum_{\pi} ( \sum_{i=1}^n |x_i a_{i,\pi(i)} |^2)^{\frac{1}{2}}$ is equivalent to a Musielak-Orlicz norm $\norm{x}_{\sum M_i}$. We also obtain the inverse result, i.e., given the Orlicz functions, we provide a formula for the choice of the matrix that generates the corresponding Musielak-Orlicz norm. As a consequence, we obtain the embedding of strictly 2-concave Musielak-Orlicz spaces into L_1. Archive classification: math.FA Mathematics Subject Classification: 46B03, 05A20, 46B45 Submitted from: prochno(a)math.uni-kiel.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.6030 or http://arXiv.org/abs/1204.6030

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Abstract of a paper by Joscha Prochno and Carsten Schuett
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "Combinatorial inequalities and subspaces of L1" by Joscha Prochno and Carsten Schuett. Abstract: Let M and N be Orlicz functions. We establish some combinatorial inequalities and show that the product spaces l^n_M(l^n_N) are uniformly isomorphic to subspaces of L_1 if M and N are "separated" by a function t^r, 1<r<2. Archive classification: math.FA math.CO Mathematics Subject Classification: 46B03, 05A20, 46B45, 46B09 Submitted from: prochno(a)math.uni-kiel.de The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.6025 or http://arXiv.org/abs/1204.6025

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Abstract of a paper by G. Botelho, D. Pellegrino, P. Rueda, J. Santos and J.B. Seoane-Sepulveda
by alspach＠math.okstate.edu 11 Jun '12

11 Jun '12

This is an announcement for the paper "When is the Haar measure a Pietsch measure for nonlinear mappings?" by G. Botelho, D. Pellegrino, P. Rueda, J. Santos and J.B. Seoane-Sepulveda. Abstract: We show that, as in the linear case, the normalized Haar measure on a compact topological group $G$ is a Pietsch measure for nonlinear summing mappings on closed translation invariant subspaces of $C(G)$. This answers a question posed to the authors by J. Diestel. We also show that our result applies to several well-studied classes of nonlinear summing mappings. In the final section some problems are proposed. Archive classification: math.FA Submitted from: dmpellegrino(a)gmail.com The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1204.5621 or http://arXiv.org/abs/1204.5621

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