Schur乘子和双算子积分的估计--小波方法
Estimates for Schur Multipliers and Double Operator Integrals -- A Wavelet Approach
摘要：
我们讨论的工作Birman和Solomyak的奇异数的积分算子的角度来看，现代逼近论，特别是使用小波技术。在$B^{\frac{1}{p}-\frac{1}{2}}_{p,p}(\mathbb R,L_2(\mathbb R))$中，我们能够给出带核积分算子范数估计的一个简单证明。这恢复，扩展和揭示了新的光Birman和Solomyak定理。我们还利用这些技巧给出了$B^{\frac{1}{p}-\frac{1}{2}}_{\frac{2p}{2-p},p}(\mathbb R,L_\infty(\mathbb R))$中符号有界的双算子积分的Schur乘子界的一个简单证明，将Birman和Solomyak的结果推广到了符号无紧域的情形.
英文摘要：
We discuss the work of Birman and Solomyak on the singular numbers of integral operators from the point of view of modern approximation theory, in particular with the use of wavelet techniques. We are able to provide a simple proof of norm estimates for integral operators with kernel in $B^{\frac{1}{p}-\frac{1}{2}}_{p,p}(\mathbb R,L_2(\mathbb R))$. This recovers, extends and sheds new light on a theorem of Birman and Solomyak. We also use these techniques to provide a simple proof of Schur multiplier bounds for double operator integrals, with bounded symbol in $B^{\frac{1}{p}-\frac{1}{2}}_{\frac{2p}{2-p},p}(\mathbb R,L_\infty(\mathbb R))$, which extends Birman and Solomyak's result to symbols without compact domain.
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