Abstract
It is shown that, under certain conditions, the bounded solutions of second-order linear elliptic differential equations are multipliers in certain weighted Hilbert spaces or in pairs of such spaces. Moreover, the role of the weight is played by a power of the distance to the boundary of the domain or by a function of the distance. This function is subjected to a condition which is necessary and sufficient for the solution to belong to the corresponding class of multipliers.
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Literature cited
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 149, pp. 165–176, 1986.
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Shaposhnikova, T.O. Bounded solutions of elliptic equations as multipliers in spaces of differentiable functions. J Math Sci 42, 1657–1665 (1988). https://doi.org/10.1007/BF01665056
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DOI: https://doi.org/10.1007/BF01665056