Abstract
The paper concerns problems of the recovery of operators from noisy information in weightedLq-spaceswithhomogeneousweights. A number of general theorems are proved and applied to finding exact constants in multidimensional Carlson type inequalities with several weights and problems of the recovery of differential operators from a noisy Fourier transform. In particular, optimal methods are obtained for the recovery of powers of generalized Laplace operators from a noisy Fourier transform in the Lp-metric.
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