Optimal recovery and generalized Carlson inequality for weights with symmetry properties
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The paper concerns problems of the recovery of operators from noisy information in weighted L_q-spaces with homogeneous weights. 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 L_p-metric.
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