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In the paper minimax rates of convergence for wavelet estimators are studied. The estimators are based on the shrinkage of empirical coefficients β_jkof wavelet decomposition of unknown function with thresholds λ_j. These thresholds depend on the regularity of the function to be estimated. In the problem of density estimation and nonparametric regression we establish upper rates of convergence over a large range of functional classes and global error measures. The constructed estimate is minimax (up to constant) for all L_πerror measures, 0 < π ≤ ∞ simultaneously.