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Bounded and Fredholm properties of SG-pseudo-differential operators in variable exponent spaces

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Abstract

This paper is devoted to the boundedness and Fredholmness of \(\mathbf{SG}\)-pseudo-differential operators with non-zero order in the Lebesgue spaces with variable exponent p(x). Moreover, we obtain a necessary and sufficient condition for \(\mathbf{SG}\)-pseudo-differential operators of the class \(\mathbf{OPSG}^{m}_{1,0}\) to be Fredholm on Sobolev spaces \(H^{s}_{p(.)}\) with constant smoothness s and variable exponent p(x).

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  1. Morteza Koozehgar Kalleji

    Present address: Department of Mathematics, Faculty of Sciences, Arak University, Arāk, 38156-8-8349, Iran

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    Koozehgar Kalleji, M. Bounded and Fredholm properties of SG-pseudo-differential operators in variable exponent spaces. J. Pseudo-Differ. Oper. Appl. 12, 33 (2021). https://doi.org/10.1007/s11868-021-00407-w

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    • DOI: https://doi.org/10.1007/s11868-021-00407-w

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