Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Carathéodory Spaces. (Record no. 69763)
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| control field | EBC3114232 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729124603.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
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| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2006 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470404611 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9780821839119 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC3114232 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL3114232 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11039851 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)922981722 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA403 -- .D36 2006eb |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 510 s;515/.2433 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Danielli, Donatella. |
| 245 10 - TITLE STATEMENT | |
| Title | Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Carathéodory Spaces. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2006. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2006. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (138 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.182 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Intro -- Contents -- Chapter 1. Introduction -- 1.1. Carnot-Carathéodory spaces -- 1.2. The Chow-Rashevsky's accessibility theorem and CC metrics -- 1.3. The Nagel-Stein-Wainger polynomial and the size of the CC balls -- Chapter 2. Carnot groups -- 2.1. Carnot groups of step 2 -- 2.2. The Kaplan mapping -- 2.3. Groups of Heisenberg type -- Chapter 3. The characteristic set -- 3.1. A result of Derridj on the size of the characteristic set -- 3.2. Some geometric examples -- 3.3. Non-characteristic manifolds -- 3.4. Manifolds with controlled characteristic set -- Chapter 4. X-variation, X-perimeter and surface measure -- 4.1. The structure of functions in BV[sub(X,loc)] -- 4.2. X-Caccioppoli sets -- 4.3. X-perimeter and the perimeter measure -- Chapter 5. Geometric estimates from above on CC balls for the perimeter measure -- 5.1. A fundamental estimate -- 5.2. The X-perimeter of a C[sup(1,1)] domain is an upper 1-Ahlfors measure -- Chapter 6. Geometric estimates from below on CC balls for the perimeter measure -- 6.1. The relative isoperimetric inequality and Theorem 6.1 -- 6.2. A basic geometric lemma -- 6.3. Further analysis for Hörmander vector fields of step 2 -- 6.4. Second proof of Theorem 6.1 -- 6.5. Failure of the 1-Ahlfors condition for the X-perimeter of C[sup(1,α)] domains -- Chapter 7. Fine differentiability properties of Sobolev functions -- 7.1. Poincaré inequality fractional integrals and improved representation formulas -- 7.2. Fine mapping properties of fractional integration on metric spaces -- 7.3. Differentiation with respect to an upper Ahlfors measure -- 7.4. Upper Ahlfors measures and Hausdorff measure -- Chapter 8. Embedding a Sobolev space into a Besov space with respect to an upper Ahlfors measure -- 8.1. Some results from harmonic analysis -- 8.2. Two simple growth-estimates. |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 8.3. A key continuity estimate for a singular integral -- 8.4. The main theorem -- Chapter 9. The extension theorem for a Besov space with respect to a lower Ahlfors measure -- 9.1. Some auxiliary results -- 9.2. Proof of Theorem 9.1 -- Chapter 10. Traces on the boundary of (ε, δ) domains -- 10.1. The (ε, δ) condition is optimal for the existence of traces -- 10.2. Characterization of the traces on the boundary -- Chapter 11. The embedding of B[sup(p)][sub(β)](Ω, dμ) into L[sup(q)](Ω, dμ) -- Chapter 12. Returning to Carnot groups -- Chapter 13. The Neumann problem -- Chapter 14. The case of Lipschitz vector fields -- Bibliography. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Harmonic analysis. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Homogeneous spaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Sobolev spaces. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Measure theory. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Differential equations, Partial. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Garofalo, Nicola. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Nhieum, Duy-Minh. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Danielli, Donatella |
| Title | Non-Doubling Ahlfors Measures, Perimeter Measures, and the Characterization of the Trace Spaces of Sobolev Functions in Carnot-Carathéodory Spaces |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2006 |
| International Standard Book Number | 9780821839119 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114232">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=3114232</a> |
| Public note | Click to View |
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