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Let λ > 0 and
$${\Delta _\lambda }: = - \frac{{{d^2}}}{{d{x^2}}} - \frac{{2\lambda }}{x}\frac{d}{{dx}}$$
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+, xdx) if and only if the Riesz transform commutator xxxx is compact on Lp(R+, x2λdx) for all p ∈ (1,∞).
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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 LpLp boundedness of these operators is established in certain cases.  相似文献   

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Bihun  Oksana  Driver  Kathy 《Numerical Algorithms》2020,85(2):503-522
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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In the present work, some general relations between Jacobi and ultraspherical polynomials are given.  相似文献   

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