Polynomial and multilinear Hardy-Littlewood inequalities: analytical and numerical approaches
نویسندگان
چکیده
منابع مشابه
Optimal Hardy–littlewood Type Inequalities for Polynomials and Multilinear Operators
Abstract. In this paper we obtain quite general and definitive forms for Hardy–Littlewood type inequalities. Moreover, when restricted to the original particular cases, our approach provides much simpler and straightforward proofs and we are able to show that in most cases the exponents involved are optimal. The technique we used is a combination of probabilistic tools and of an interpolative a...
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We establish conditions under which the extended Hardy-Littlewood inequality ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx ≤ ∫ RN H ( |x|, u1(x), . . . , um(x) ) dx, where each ui is non-negative and u ∗ i denotes its Schwarz symmetrization, holds. We also determine appropriate monotonicity assumptions on H such that equality occurs in the above inequality if and only if each ui is Schwarz symmetric....
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Let {cj} be a null sequence of bounded variation. We give appreciate smoothness and growth conditions on {cj} to obtain the pointwise convergence as well as Lr -convergence of Laguerre series ∑ cj a j . Then, we prove aHardy-Littlewood type inequality ∫∞ 0 |f(t)|r dt≤ C ∑∞ j=0 |cj| j̄1−r/2 for certain r ≤ 1, where f is the limit function of ∑ cj a j . Moreover, we show that if f(x) ∼ ∑cj a j is ...
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We investigate the growth of the constants of the polynomial Hardy-Littlewood inequality.
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Let T be a Calderon-Zygmund operator, a classical result of Coifman, Rochberg and Weiss (see [7]) states that the commutator [b, T ] = T (bf)−bTf (where b ∈ BMO(Rn)) is bounded on Lp(Rn) for 1 < p < ∞; Chanillo (see [2]) proves a similar result when T is replaced by the fractional integral operator. However, it was observed that [b, T ] is not bounded, in general, from Hp(Rn) to Lp(Rn) for p ≤ ...
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ژورنال
عنوان ژورنال: Mathematical Inequalities & Applications
سال: 2018
ISSN: 1331-4343
DOI: 10.7153/mia-2018-21-24