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Littlewood-Paley Theory on Spaces of Homogeneous Type and the Classical Function Spaces
Y. S. Han and E. T. Sawyer
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Memoirs of the American Mathematical Society
1994; 126 pp; softcover
Volume: 110
ISBN-10: 0-8218-2592-5
ISBN-13: 978-0-8218-2592-1
List Price: US$40
Individual Members: US$24
Institutional Members: US$32
Order Code: MEMO/110/530
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In this work, Han and Sawyer extend Littlewood-Paley theory, Besov spaces, and Triebel-Lizorkin spaces to the general setting of a space of homogeneous type. For this purpose, they establish a suitable analogue of the Calderón reproducing formula and use it to extend classical results on atomic decomposition, interpolation, and T1 and Tb theorems. Some new results in the classical setting are also obtained: atomic decompositions with vanishing b-moment, and Littlewood-Paley characterizations of Besov and Triebel-Lizorkin spaces with only half the usual smoothness and cancellation conditions on the approximate identity.

Readership

Research mathematicians.

Table of Contents

  • Introduction
  • \(T_N^{-1}\) is a Calderón-Zygmund operator
  • The Calderón-type reproducing formula on spaces of homogeneous type
  • The Besov and Triebel-Lizorkin spaces on spaces of homogeneous type
  • The \(T1\) theorems of \(\dot B_p^{\alpha ,q}\) and \(\dot F_p^{\alpha ,q}\)
  • Atomic decomposition of \(\dot B_p^{\alpha ,q}\) and \(\dot F_p^{\alpha ,q}\)
  • Duality and interpolation of \(\dot B_p^{\alpha ,q}\) and \(\dot F_p^{\alpha ,q}\)
  • References
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