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Spline Representations of Lizorkin–Triebel Spaces with General Weights

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Abstract

In this paper we introduce some new Lizorkin–Triebel type spaces of variable smoothness. Here the smoothness lies in a new weighted class. We give some equivalent quasinorms and their characterizations via oscillations. We show that the box splines and tensor-products of \( B \)-splines are suitable to obtain the stable representations of functions of these spaces.

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Acknowledgments

The author thanks W. Sickel and A. Tyulenev for making several useful suggestions and comments that improved the paper substantially and simplify some proofs. Also, the author gratefully appreciates the anonymous referee for the constructive comments and recommendations that definitely helped improve the readability and quality of the paper.

Funding

This work was supported by the General Directorate of Scientific Research and Technological Development of Algeria and the General Direction of Higher Education and Training (Grant no. C00L03UN280120220004).

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  1. Laboratory of Functional Analysis and Geometry of Spaces, Department of Mathematics, M’sila University, M’sila, Algeria

    D. Drihem

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  1. D. Drihem
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Correspondence to D. Drihem.

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Drihem, D. Spline Representations of Lizorkin–Triebel Spaces with General Weights. Sib Math J 64, 208–250 (2023). https://doi.org/10.1134/S0037446623010202

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