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We characterize a weighted norm inequality which corresponds to the embeddingof a class of absolutely continuous functions into the fractional order Sobolevspace. The auxiliary result of the paper is of independent interest. Itcomprises of several types of necessary and sufficient conditions for theboundedness of the Hardy--Steklov operator (an integral operator with twovariable boundaries of integration) in weighted Lebesgue spaces.

Hardy-Steklov operators and embedding inequalities of Sobolev type