The Resource Boundedness results for operators with singular kernels on distribution spaces
Boundedness results for operators with singular kernels on distribution spaces
Resource Information
The item Boundedness results for operators with singular kernels on distribution spaces represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.This item is available to borrow from 1 library branch.
Resource Information
The item Boundedness results for operators with singular kernels on distribution spaces represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Liverpool.
This item is available to borrow from 1 library branch.
- 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
- Language
- eng
- Extent
- viii, 172 pages
- 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
- Isbn
- 9780821825051
- Label
- Boundedness results for operators with singular kernels on distribution spaces
- Title
- Boundedness results for operators with singular kernels on distribution spaces
- 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
- 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
- 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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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.liverpool.ac.uk/portal/Boundedness-results-for-operators-with-singular/uJGFfURBmsg/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.liverpool.ac.uk/portal/Boundedness-results-for-operators-with-singular/uJGFfURBmsg/">Boundedness results for operators with singular kernels on distribution spaces</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.liverpool.ac.uk/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.liverpool.ac.uk/">University of Liverpool</a></span></span></span></span></div>
