rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Hardy Spaces on the Euclidean Space
  name:
    name part: Uchiyama, Akihito.
    role:
      role term: creator
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: Electronic books.
  origin info:
    place:
      place term: ja
    date issued: 2001
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (XIII, 282 pages)
  abstract: "Still waters run deep." This proverb expresses exactly how a mathematician Akihito Uchiyama and his works were. He was not celebrated except in the field of harmonic analysis, and indeed he never wanted that. He suddenly passed away in summer of 1997 at the age of 48. However, nowadays his contributions to the fields of harmonic analysis and real analysis are permeating through various fields of analysis deep and wide. One could write several papers explaining his contributions and how they have been absorbed into these fields, developed, and used in further breakthroughs. Peter W. Jones (Professor of Yale University) says in his special contribution to this book that Uchiyama's decomposition of BMO functions is considered to be the Mount Everest of Hardy space theory. This book is based on the draft, which the author Akihito Uchiyama had completed by 1990. It deals with the theory of real Hardy spaces on the n-dimensional Euclidean space. Here the author explains scrupulously some of important results on Hardy spaces by real-variable methods, in particular, the atomic decomposition of elements in Hardy spaces and his constructive proof of the Fefferman-Stein decomposition of BMO functions into the sum of a bounded?function and Riesz transforms of bounded functions.
  table of contents: Foreword -- Recollections of My Good Friend, Akihito Uchiyama by Peter W. Jones -- Preface -- Introduction -- Lipschitz spaces and BMO -- Atomic Hp sapces -- Atomic decomposition from grand maximal functions -- Atomic decomposition from S functions -- Hardy-Littlewood-Fefferman-Stein type inequalities, 1 -- Hardy-Littlewood-Fefferman-Stein type inequalities, 2 -- Hardy-Littlewood-Fefferman-Stein type inequalities, 3 -- Grand maximal function from radial maximal functions -- S-functions from g-functions Good lambda inequalities for nontangential maximal functions and S-functions of harmonic functions -- A direct proof (special characters) -- A direct proof of (special characters) -- Subharmonicity 1 -- Subharmonicity 2 -- Preliminaries for characterizations of H in terms of Fourier multipliers -- Characterization of Hp in terms of Riesz transforms -- Other results on the characterization of Hp in terms of Fourier multipliers -- Fefferman's original proof of (special characters) -- Varopoulos's proof of the above inequality -- The Fefferman-Stein decomposition of BMO -- A constructive proof of the Fefferman-Stein decomposition of BMO -- Vector-valued unimodular BMO functions -- Extensions of the Fefferman-Stein decomposition of BMO, 1 -- Characterization of H1 in terms of Fourier multipliers -- Extension of the Fefferman-Stein decomposition of BMO, 2 -- Characterization of Hp in terms of Fourier multipliers -- The one-dimensional case -- Appendix -- References -- Index.
  note: edited by Akihito Uchiyama.
  note: Electronic resource.
  subject:
    topic: Mathematics
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Number theory
  subject:
    topic: Geometry, Algebraic
  subject:
    topic: Mathematics
  subject:
    topic: Number theory
  classification: QA241-247.5
  classification: 512.7
  related item:
    title info:
      title: Springer monographs in mathematics
  identifier: 9784431679059 (electronic bk.)
  identifier: 4431679057 (electronic bk.)
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: I9W
    record creation date: 121227
    record change date: 20260422200633.3
    record identifier: in00003543604
    language of cataloging:
      language term: eng