Improving Estimates for Discrete Polynomial Averages
نویسندگان
چکیده
منابع مشابه
L-improving estimates for averages on polynomial curves
In the combinatorial method proving of Lp-improving estimates for averages along curves pioneered by Christ [6], it is desirable to estimate the average modulus (with respect to some uniform measure on a set) of a polynomial-like function from below using only the value of the function or its derivatives at some prescribed point. In this paper, it is shown that there is always a relatively larg...
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In the combinatorial method proving of Lp-improving estimates for averages along curves pioneered by Christ [8], it is desirable to estimate the average modulus (with respect to some uniform measure on a set) of a polynomial-like function from below using only the value of the function or its derivatives at some prescribed point. In this paper, it is shown that there is always a relatively larg...
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We establish local (L, L) mapping properties for averages on curves. The exponents are sharp except for endpoints.
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Let n ≥ 2, and let M1 and M2 be two smooth n − 1-dimensional manifolds, each containing a preferred origin 0M1 and 0M2 . We shall abuse notation and write 0 for both 0M1 and 0M2 . For the purposes of integration we shall place a smooth Riemannian metric on M1 and M2, although the exact choice of this metric will not be relevant. All our considerations shall be local to the origin 0. We are inte...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2020
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-020-09748-4