Displaying similar documents to “The fundamental principle and some of its applications”

Some remarks on restriction of the Fourier tranform for general measures.

Per Sjölin, Fernando Soria (1999)

Publicacions Matemàtiques

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In this paper we establish a formal connection between the average decay of the Fourier transform of functions with respect to a given measure and the of that measure. We also present a generalization of the classical restriction theorem of Stein and Tomas replacing the sphere with sets of prefixed Hausdorff dimension n - 1 + α, with 0 < α < 1.

Multiparameter singular integrals and maximal functions

Fulvio Ricci, Elias M. Stein (1992)

Annales de l'institut Fourier

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We prove L p -boundedness for a class of singular integral operators and maximal operators associated with a general k -parameter family of dilations on R n . This class includes homogeneous operators defined by kernels supported on homogeneous manifolds. For singular integrals, only certain “minimal” cancellation is required of the kernels, depending on the given set of dilations.

Multivariate moment problems : geometry and indeterminateness

Mihai Putinar, Claus Scheiderer (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The most accurate determinateness criteria for the multivariate moment problem require the density of polynomials in a weighted Lebesgue space of a generic representing measure. We propose a relaxation of such a criterion to the approximation of a single function, and based on this condition we analyze the impact of the geometry of the support on the uniqueness of the representing measure. In particular we show that a multivariate moment sequence is determinate if its support has dimension...