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The Resource Boundedness results for operators with singular kernels on distribution spaces

Boundedness results for operators with singular kernels on distribution spaces

Label
Boundedness results for operators with singular kernels on distribution spaces
Title
Boundedness results for operators with singular kernels on distribution spaces
Creator
Subject
Language
eng
Summary
In this monograph, the author generalizes the T1 theorem of G. David and J.-L. Journé to the context of Triebel-Lizorkin spaces, which include most of the function and distribution spaces of importance in classical analysis. M. Frazier and B. Jawerth have shown that these spaces admit decompositions in terms of certain fundamental building blocks, known as "smooth atoms'' and "smooth molecules''. In the author's words, "to prove that an operator is bounded on a Triebel-Lizorkin space, it is enough to show that it maps every family of smooth atoms into a family of smooth molecules''. The same basic techniques can be used to study operators between two different Triebel-Lizorkin spaces. Results are obtained for a wide variety of operators acting on the Triebel-Lizorkin spaces, including generalized Calderón-Zygmund operators and their derivatives; potential operators; fractional integral operators; and the Hörmander classes of pseudodifferential operators. When these general results are restricted to specific spaces, many classical boundedness results are recovered
Cataloging source
UkLiU
http://library.link/vocab/creatorDate
1960-
http://library.link/vocab/creatorName
Torres, Rodolfo H.
Series statement
Memoirs of the American Mathematical Society
Series volume
442
http://library.link/vocab/subjectName
  • Decomposition method
  • Theory of distributions (Functional analysis)
  • Pseudodifferential operators
Label
Boundedness results for operators with singular kernels on distribution spaces
Instantiates
Publication
Bibliography note
Includes notes on notation, and bibliographical references (pages 169-172)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Introduction
  • The atomic decomposition of the Triebel-Lizorkin spaces
  • Generalized Calderón-Zygmund operators
  • Generalized Calderón-Zygmund operators on Triebel-Lizorkin spaces
  • Operators with singular kernels of different sizes
  • Pseudodifferential operators on Triebel-Lizorkin spaces
Dimensions
26 cm.
Extent
viii, 172 pages
Isbn
9780821825051
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations
Label
Boundedness results for operators with singular kernels on distribution spaces
Publication
Bibliography note
Includes notes on notation, and bibliographical references (pages 169-172)
Carrier category
volume
Carrier category code
  • nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Contents
  • Introduction
  • The atomic decomposition of the Triebel-Lizorkin spaces
  • Generalized Calderón-Zygmund operators
  • Generalized Calderón-Zygmund operators on Triebel-Lizorkin spaces
  • Operators with singular kernels of different sizes
  • Pseudodifferential operators on Triebel-Lizorkin spaces
Dimensions
26 cm.
Extent
viii, 172 pages
Isbn
9780821825051
Media category
unmediated
Media MARC source
rdamedia
Media type code
  • n
Other physical details
illustrations

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      53.418074 -2.967913
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