Sobolev及Besov空间中Bochner-Riesz算子的逼近
Approximation of Bochner-Riesz operators in weighted Sobolev and Besov spaces
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摘要: 研究了第一类Chebyshev加权正交多项式的Riesz算子，利用 K-泛函对加权Sobolev空间中函数进行逼近研究，证明了Bochner-Riesz算子在
L_W^p −1, 1 空间中的有界性，得到了 K-泛函控制估计，进一步得到对加权Besov空间的刻画.Abstract: We study the Riesz operator of the first kind of Chebyshev weighted orthogonal polynomials. Using K-functional, we discuss the approximation of Bochner-Riesz operators in the weighted Sobolev space. We prove the bounded of Bochner-Riesz operators inL_W^p - 1, 1 space, obtain the K-functional control estimation, and further characterize the weighted Besov space.
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