23 research outputs found

    Abstract Ces\`aro spaces: Integral representations

    Full text link
    The Ces\`aro function spaces Cesp=[C,Lp]Ces_p=[C,L^p], 1≤p≤∞1\le p\le\infty, have received renewed attention in recent years. Many properties of [C,Lp][C,L^p] are known. Less is known about [C,X][C,X] when the Ces\`aro operator takes its values in a rearrangement invariant (r.i.) space XX other than LpL^p. In this paper we study the spaces [C,X][C,X] via the methods of vector measures and vector integration. These techniques allow us to identify the absolutely continuous part of [C,X][C,X] and the Fatou completion of [C,X][C,X]; to show that [C,X][C,X] is never reflexive and never r.i.; to identify when [C,X][C,X] is weakly sequentially complete, when it is isomorphic to an AL-space, and when it has the Dunford-Pettis property. The same techniques are used to analyze the operator C:[C,X]→XC:[C,X]\to X; it is never compact but, it can be completely continuous.Comment: 21 page

    A note on extreme points of the unit of Hardy-Lorentz spaces

    Full text link
    We show that inner functions are extreme points of the unit ball of the Hardy-Lorentz space H(Λ(φ))H(\Lambda(\varphi)), for Λ(φ)\Lambda(\varphi) a Lorentz space with φ\varphi strictly increasing and strictly concave.Comment: This is the final version, to be published in the Proceedings of the American Mathematical Societ

    Fine spectra of the finite Hilbert transform in function spaces

    Full text link
    We investigate the spectrum and fine spectra of the finite Hilbert transform acting on rearrangement invariant spaces over (−1,1)(-1,1) with non-trivial Boyd indices, thereby extending Widom's results for LpL^p spaces. In the case when these indices coincide, a full description of the spectrum and fine spectra is given.Comment: 26 pages, 1 figure. Minor changes from previous version. This is the final version, to be published in Advances in Mathematic

    A note on function spaces generated by Rademacher series

    Get PDF

    The finite Hilbert transform on (−1,1)(-1,1)

    Full text link
    We present a detailed survey of recent developments in the study of the finite Hilbert transform and its corresponding inversion problem in rearrangement invariant spaces on (−1,1)(-1,1)

    Giovanni Battista Guccia: pioneer of international cooperation in mathematics

    No full text
    This book examines the life and work of mathematician Giovanni Battista Guccia, founder of the Circolo Matematico di Palermo and its renowned journal, the Rendiconti del Circolo matematico di Palermo. The authors describe how Guccia, an Italian geometer, was able to establish a mathematical society in Sicily in the late nineteenth century, which by 1914 would grow to become the largest and most international in the world, with one of the most influential journals of the time. The book highlights the challenges faced by Guccia in creating an international society in isolated Palermo, and places Guccia’s activities in the wider European context through comparisons with the formation of the London Mathematical Society and the creation of Mittag-Leffler’s Acta Mathematica in Stockholm. Based on extensive searches in European archives, this scholarly work follows both historical and scientific treads, and will appeal to those interested in the history of mathematics and science in general
    corecore