共查询到10条相似文献,搜索用时 62 毫秒
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Let λ > 0 and be the Bessel operator on R+:= (0,∞). We first introduce and obtain an equivalent characterization of CMO(R+, x2λdx). By this equivalent characterization and by establishing a new version of the Fréchet-Kolmogorov theorem in the Bessel setting, we further prove that a function b ∈ BMO(R+, x2λdx) is in CMO(R+, x2λdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).
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$${\Delta _\lambda }: = - \frac{{{d^2}}}{{d{x^2}}} - \frac{{2\lambda }}{x}\frac{d}{{dx}}$$
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We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on via the special form of the representation of the derivatives by
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Analogues of Riesz potentials and Riesz transforms are defined and studied for the Dunkl transform associated with a family of weight functions that are invariant under a reflection group. The Lp boundedness of these operators is established in certain cases. 相似文献
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Numerical Algorithms - Let $\displaystyle \{x_{k,n-1}\}_{k=1}^{n-1}$ and $\displaystyle \{x_{k,n}\}_{k=1}^{n},$ $n \in \mathbb {N}$ , be two sets of real, distinct points satisfying the interlacing... 相似文献
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H.V Hòa 《Journal of Mathematical Analysis and Applications》1981,82(2):392-398
In the present work, some general relations between Jacobi and ultraspherical polynomials are given. 相似文献
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Journal d'Analyse Mathématique - 相似文献