Multilinear Marcinkiewicz-Zygmund Inequalities
نویسندگان
چکیده
منابع مشابه
Marcinkiewicz-Zygmund inequalities
We study a generalization of the classical Marcinkiewicz-Zygmund inequalities. We relate this problem to the sampling sequences in the Paley-Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz-Zygmund inequalities.
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Recently, norm equivalences between spherical polynomials and their sample values at scattered sites have been proved. These so-called MarcinkiewiczZygmund inequalities involve a parameter that characterizes the density of the sampling set and they are applicable to all polynomials whose degree does not exceed an upper bound that is determined by the density parameter. We show that if one is sa...
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We obtain converse Marcinkiewicz-Zygmund inequalities such as k P kLp[ 1;1] C 0@ n X j=1 j jP (tj)j 1A1=p for polynomials P of degree n 1, under general conditions on the points ftjgj=1 and on the function . The weights f jgj=1 are appropriately chosen. We illustrate the results by applying them to extended Lagrange interpolation for exponential weights on [ 1; 1].
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Geodetic and meteorological data, collected via satellites for example, are genuinely scattered, and not confined to any special set of points. Even so, known quadrature formulas used in numerically computing integrals involving such data have had restrictions either on the sites (points) used or, more significantly, on the number of sites required. Here, for the unit sphere embedded in Rq, we ...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2017
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-017-9563-5