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Restricted Boundedness of Translation Operators on Variable Lebesgue Spaces

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Current Trends in Analysis, its Applications and Computation

Part of the book series: Trends in Mathematics ((RESPERSP))

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Abstract

In this paper, we investigate the inequality

$$\displaystyle \left \Vert f(\cdot +h)\right \Vert { }_{p\left ( \cdot \right ) }\leq A\left \Vert f\right \Vert { }_{p\left ( \cdot \right ) },\quad h\in \mathbb {R}^{n}, A>0 $$

under some suitable assumptions on the function f and the variable exponent p.

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Acknowledgements

We thank the referee for carefully reading the paper and for making several useful suggestions and comments, which improved the exposition of the paper substantially.

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Authors and Affiliations

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

    Douadi Drihem

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  1. Douadi Drihem
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Correspondence to Douadi Drihem .

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Editors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Paula Cerejeiras

  2. Institut of Applied Analysis, TU Bergakademie Freiberg, Freiberg, Germany

    Michael Reissig

  3. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Irene Sabadini

  4. Department of Mathematics, Linnaeus University, Växjö, Sweden

    Joachim Toft

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Drihem, D. (2022). Restricted Boundedness of Translation Operators on Variable Lebesgue Spaces. In: Cerejeiras, P., Reissig, M., Sabadini, I., Toft, J. (eds) Current Trends in Analysis, its Applications and Computation. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-87502-2_33

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