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Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction
Let S be a hypersurface in which is the graph of a smooth, finite type function φ , and let μ = ρ dσ be a surface carried measure on S , where dσ denotes the surface element on S and ρ a smooth density with sufficiently small support. We derive uniform estimates for the Fourier transform of μ , wh...
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| Published in: | The Journal of fourier analysis and applications 2011-12, Vol.17 (6), p.1292-1332 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c1994-d89d2bf474d76427b08b55781c8291d8d5abc94b9fb5701d170cd1bf4a36fda43 |
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| cites | cdi_FETCH-LOGICAL-c1994-d89d2bf474d76427b08b55781c8291d8d5abc94b9fb5701d170cd1bf4a36fda43 |
| container_end_page | 1332 |
| container_issue | 6 |
| container_start_page | 1292 |
| container_title | The Journal of fourier analysis and applications |
| container_volume | 17 |
| creator | Ikromov, Isroil A. Müller, Detlef |
| description | Let
S
be a hypersurface in
which is the graph of a smooth, finite type function
φ
, and let
μ
=
ρ
dσ
be a surface carried measure on
S
, where
dσ
denotes the surface element on
S
and
ρ
a smooth density with sufficiently small support. We derive uniform estimates for the Fourier transform
of
μ
, which are sharp except for the case where the principal face of the Newton polyhedron of
φ
, when expressed in adapted coordinates, is unbounded. As an application, we prove a sharp
L
p
-
L
2
Fourier restriction theorem for
S
in the case where the original coordinates are adapted to
φ
. This improves on earlier joint work with M. Kempe. |
| doi_str_mv | 10.1007/s00041-011-9191-4 |
| format | article |
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S
be a hypersurface in
which is the graph of a smooth, finite type function
φ
, and let
μ
=
ρ
dσ
be a surface carried measure on
S
, where
dσ
denotes the surface element on
S
and
ρ
a smooth density with sufficiently small support. We derive uniform estimates for the Fourier transform
of
μ
, which are sharp except for the case where the principal face of the Newton polyhedron of
φ
, when expressed in adapted coordinates, is unbounded. As an application, we prove a sharp
L
p
-
L
2
Fourier restriction theorem for
S
in the case where the original coordinates are adapted to
φ
. This improves on earlier joint work with M. Kempe.</description><identifier>ISSN: 1069-5869</identifier><identifier>EISSN: 1531-5851</identifier><identifier>DOI: 10.1007/s00041-011-9191-4</identifier><language>eng</language><publisher>Boston: SP Birkhäuser Verlag Boston</publisher><subject>Abstract Harmonic Analysis ; Approximations and Expansions ; Fourier Analysis ; Mathematical Methods in Physics ; Mathematics ; Mathematics and Statistics ; Partial Differential Equations ; Signal,Image and Speech Processing</subject><ispartof>The Journal of fourier analysis and applications, 2011-12, Vol.17 (6), p.1292-1332</ispartof><rights>Springer Science+Business Media, LLC 2011</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c1994-d89d2bf474d76427b08b55781c8291d8d5abc94b9fb5701d170cd1bf4a36fda43</citedby><cites>FETCH-LOGICAL-c1994-d89d2bf474d76427b08b55781c8291d8d5abc94b9fb5701d170cd1bf4a36fda43</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,780,784,27924,27925</link.rule.ids></links><search><creatorcontrib>Ikromov, Isroil A.</creatorcontrib><creatorcontrib>Müller, Detlef</creatorcontrib><title>Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction</title><title>The Journal of fourier analysis and applications</title><addtitle>J Fourier Anal Appl</addtitle><description>Let
S
be a hypersurface in
which is the graph of a smooth, finite type function
φ
, and let
μ
=
ρ
dσ
be a surface carried measure on
S
, where
dσ
denotes the surface element on
S
and
ρ
a smooth density with sufficiently small support. We derive uniform estimates for the Fourier transform
of
μ
, which are sharp except for the case where the principal face of the Newton polyhedron of
φ
, when expressed in adapted coordinates, is unbounded. As an application, we prove a sharp
L
p
-
L
2
Fourier restriction theorem for
S
in the case where the original coordinates are adapted to
φ
. This improves on earlier joint work with M. Kempe.</description><subject>Abstract Harmonic Analysis</subject><subject>Approximations and Expansions</subject><subject>Fourier Analysis</subject><subject>Mathematical Methods in Physics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Partial Differential Equations</subject><subject>Signal,Image and Speech Processing</subject><issn>1069-5869</issn><issn>1531-5851</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2011</creationdate><recordtype>article</recordtype><recordid>eNp9kEtOwzAQhi0EEqVwAHa-QMCT2HG8rKoWKhUhQbu2HD_AVetUdrronmtwOU6CQxFLFqN5fqOZH6FbIHdACL9PhBAKBQEoBAgo6BkaAaugYA2D8xyTWuS4FpfoKqUNISVUvBqh4zp418UdnqXe71RvE84p7t8tnneH6G3Eq6hC-pnpHH49RKe0xVMVc9PgJ6vSIWbKB_z18VlhFUw2PNnvt16r3ncB993frheb-uj1UL5GF05tk7359WO0ns9W08di-fywmE6WhQYhaGEaYcrWUU4Nr2nJW9K0jPEGdFMKMI1hqtWCtsK1jBMwwIk2kAFV1c4oWo0RnPbq2KUUrZP7mD-NRwlEDtrJk3YyaycH7eTAlCcm5dnwZqPc5AdCPvMf6BtO_XP0</recordid><startdate>201112</startdate><enddate>201112</enddate><creator>Ikromov, Isroil A.</creator><creator>Müller, Detlef</creator><general>SP Birkhäuser Verlag Boston</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>201112</creationdate><title>Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction</title><author>Ikromov, Isroil A. ; Müller, Detlef</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c1994-d89d2bf474d76427b08b55781c8291d8d5abc94b9fb5701d170cd1bf4a36fda43</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2011</creationdate><topic>Abstract Harmonic Analysis</topic><topic>Approximations and Expansions</topic><topic>Fourier Analysis</topic><topic>Mathematical Methods in Physics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Partial Differential Equations</topic><topic>Signal,Image and Speech Processing</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ikromov, Isroil A.</creatorcontrib><creatorcontrib>Müller, Detlef</creatorcontrib><collection>CrossRef</collection><jtitle>The Journal of fourier analysis and applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ikromov, Isroil A.</au><au>Müller, Detlef</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction</atitle><jtitle>The Journal of fourier analysis and applications</jtitle><stitle>J Fourier Anal Appl</stitle><date>2011-12</date><risdate>2011</risdate><volume>17</volume><issue>6</issue><spage>1292</spage><epage>1332</epage><pages>1292-1332</pages><issn>1069-5869</issn><eissn>1531-5851</eissn><abstract>Let
S
be a hypersurface in
which is the graph of a smooth, finite type function
φ
, and let
μ
=
ρ
dσ
be a surface carried measure on
S
, where
dσ
denotes the surface element on
S
and
ρ
a smooth density with sufficiently small support. We derive uniform estimates for the Fourier transform
of
μ
, which are sharp except for the case where the principal face of the Newton polyhedron of
φ
, when expressed in adapted coordinates, is unbounded. As an application, we prove a sharp
L
p
-
L
2
Fourier restriction theorem for
S
in the case where the original coordinates are adapted to
φ
. This improves on earlier joint work with M. Kempe.</abstract><cop>Boston</cop><pub>SP Birkhäuser Verlag Boston</pub><doi>10.1007/s00041-011-9191-4</doi><tpages>41</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 1069-5869 |
| ispartof | The Journal of fourier analysis and applications, 2011-12, Vol.17 (6), p.1292-1332 |
| issn | 1069-5869 1531-5851 |
| language | eng |
| recordid | cdi_crossref_primary_10_1007_s00041_011_9191_4 |
| source | Springer Nature |
| subjects | Abstract Harmonic Analysis Approximations and Expansions Fourier Analysis Mathematical Methods in Physics Mathematics Mathematics and Statistics Partial Differential Equations Signal,Image and Speech Processing |
| title | Uniform Estimates for the Fourier Transform of Surface Carried Measures in ℝ3 and an Application to Fourier Restriction |
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