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We investigate the functions spaces on ℝn for which the generalized partial derivatives Dkrkf exist and belong to different Lorentz spaces Λpk,sk(w), where pk>1 and w is nonincreasing and satisfies some special conditions. For the functions in these weighted Sobolev-Lorentz spaces, the estimates of the Besov type norms are found. The methods used in the paper are based on some estimates of nonincreasing rearrangements and the application of Bp, Bp,∞ weights.