International Mathematics Research Notices

International Mathematics Research Notices (2008) Vol. 2008 : article ID rnm154, 18 pages, doi:10.1093/imrn/rnm154 published on February 6, 2008

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Equivalent norms for polynomials on the sphere

Jordi Marzo and Joaquim Ortega-Cerdà¹

¹ Departament de Matemàtica Aplicada i Anàlisi Universitat de Barcelona, Gran via 585, 08071 Barcelona, Spain

Correspondence: Correspondence to be sent to: jmarzo{at}mat.ub.es

We find necessary and sufficient conditions for a sequence of sets E_L ^d in order to obtain the inequality

where 1 p < +, Q_L is any polynomial of degree smaller or equal than L, µ is a doubling measure, and the constant C_p is independent of L. From this description, it follows an uncertainty principle for functions in L²(^d). We also consider weighted uniform versions of this result.

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This Article Abstract Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Add to My Personal Archive Download to citation manager Request Permissions How to cite this article Google Scholar Articles by Marzo, J. Articles by Ortega-Cerdà, J. Search for Related Content Social Bookmarking          What's this?