Orthogonal Systems of Spline Wavelets as Unconditional Bases in Sobolev Spaces

Rajula Srivastava

备注：: 21 pages, 1 figure

英文摘要：

We exhibit the necessary range for which functions in the Sobolev spaces $L^s_p$ can be represented as an unconditional sum of orthonormal spline wavelet systems, such as the Battle-Lemarié wavelets. We also consider the natural extensions to Triebel-Lizorkin spaces. This builds upon, and is a generalization of, previous work of Seeger and Ullrich, where analogous results were established for the Haar wavelet system.

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