最近, 我们得到了单位圆盘Qp空间中的Jackson 定理, 进一步建立其逆定理(Bernstein 定理). 为此, 需要建立Qp空间中的Bernstein不等式和Qp空间范数的无导数特征刻画.后者的推导将利用Riesz插值公式, 该公式将导数算子表示为平移算子.作为应用, 给出了Qp空间中的Lipschitz和Zygmund子空间的利用逼近表达的等价刻画.
Abstract
In Qp spaces in the unit disc of the complex plane, the Jackson theorem has been established recently. In this article we further consider its inverse theorem, i.e., the Bernstein theorem. This will require the Qp version of the Beinstein inequality and a derivative-free characterization for Qp norm. The derivative-free characterization is realized by invoking the Riesz interpolation formula which interprets derivative as translation operators. As applications, the Lipschitz and Zygmund subspaces in Qp spaces can be characterized in terms of rates of approximation.
关键词
Qp空间 /
Bernstein定理 /
Bernstein不等式 /
Riesz插值公式
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Key words
Qp spaces /
Bernstein's theorem /
Bernstein's inequality /
Riesz interpolation formula
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参考文献
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脚注
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基金
国家自然科学基金(11371337)及博士点基金项目(20123402110068);河北省自然科学基金(A2015207007)及省教育厅科研基金(QN20131027);河北经贸大学科研基金(2013KYQ07)
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