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On the composition operators on Besov and Triebel–Lizorkin spaces with power weights

Volume 129 / 2022

Douadi Drihem Annales Polonici Mathematici 129 (2022), 117-137 MSC: Primary 47H30; Secondary 46E35. DOI: 10.4064/ap220314-23-9 Published online: 8 November 2022

Abstract

Let be a continuous function. Under some assumptions on G, s,\alpha ,p and q we prove that \{G(f):f\in A_{p,q}^{s}(\mathbb R^{n},|\cdot |^{\alpha })\}\subset A_{p,q}^{s}(\mathbb R^{n},|\cdot |^{\alpha }) implies that G is a linear function. Here A_{p,q}^{s}(\mathbb R^{n},|\cdot |^{\alpha }) stands either for the Besov space B_{p,q}^{s}(\mathbb R^{n},|\cdot |^{\alpha }) or for the Triebel–Lizorkin space F_{p,q}^{s}(\mathbb R^{n},|\cdot |^{\alpha }). These spaces unify and generalize many classical function spaces such as Sobolev spaces with power weights.

Authors

  • Douadi DrihemLaboratory of Functional Analysis and Geometry of Spaces
    Department of Mathematics
    M’sila University
    M’sila 28000, Algeria
    e-mail
    e-mail

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