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INICIO | 29 de marzo de 2024
  

Measure-preserving quality within mappings.

Título inglés Measure-preserving quality within mappings.
Título español Cualidad conservadora de la medida en aplicaciones.
Autor/es Semmes, Stephen
Organización Dep. Math. Rice Univ., Houston (Texas), Estados Unidos
Revista 0213-2230
Publicación 2000, 16 (2): 363-458, 27 Ref.
Tipo de documento articulo
Idioma Inglés
Resumen inglés In [6], Guy David introduced some methods for finding controlled behavior in Lipschitz mappings with substantial images (in terms of measure). Under suitable conditions, David produces subsets on which the given mapping is bilipschitz, with uniform bounds for the bilipschitz constant and the size of the subset. This has applications for boundedness of singular integral operators and uniform rectifiability of sets, as in [6], [7], [11], [13]. Some special cases of David's results, concerning projections of subsets of Euclidean spaces of codimension 1, or mappings defined on Euclidean spaces (rather than sets or metric spaces of less simple nature), have been given alternate and much simpler proofs as in [8], [19], [10]. In general, this has not occurred.
Here we shall present a variation of David's methods which breaks down into simpler pieces. We shall also take advantage of some components of the work of Peter Jones [19]. Jones' approach uses some Littlewood-Paley theory, and one of the important features of David's method was to avoid this, operating in a more directly geometric way which could be applied more broadly. To some extent, the present organization gives a reconciliation between the two, and between David's stopping-time argument and techniques related to Carleson measures and Carleson's Corona construction.
Clasificación UNESCO 121009
Palabras clave español Aplicación lipschitziana ; Integrales singulares ; Espacios métricos
Código MathReviews MR1809345
Código Z-Math Zbl 1041.42014
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Equipo DML-E
Instituto de Ciencias Matemáticas (ICMAT - CSIC)
rmm()icmat.es