Orthogonal systems of spline wavelets as unconditional bases in Sobolev spaces

Rajula Srivastava

Mathematische Nachrichten, 2023, vol. 296, issue 2, 853-875

Abstract: We exhibit the necessary range for which functions in the Sobolev spaces Lps$L^s_p$ 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.

Date: 2023
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