Tohoku Mathematical Journal, Second Series
Online ISSN : 2186-585X
Print ISSN : 0040-8735
ISSN-L : 0040-8735
ON SHARPNESS, APPLICATIONS AND GENERALIZATIONS OF SOME CARLEMAN TYPE INEQUALITIES
LJUBOMIR T. DECHEVSKYLARS-ERIK PERSSON
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1996 Volume 48 Issue 1 Pages 1-22

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Abstract
Carleman's inequality for Hilbert-Schmidt operators and its generalizations for Schatten-von Neumann operator ideals (see [7]) are shown to be sharp in a certain sense. Explicit classes of extremizing operators are found on which the generalized Carleman inequalities turn to asymptotic equalities. Applications are made to a priori estimation of the solutions of Fredholm and Volterra first- and second kind integral equations and to perturbation and error analysis. Some further generalizations are considered which extend the applications to singular integral equations, pseudodifferential equations and analytic functions of operator argument.
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