Abstract. The multidimensional generalization of the Lupas--Ostrowski inequality, bounding the Chebyshev functional for the functions whose derivatives are square integrable, is given.

AMS Subject Classification (1991): 26D15

Keyword(s): The Chebyshev functional, the Fourier expansion, square integrable functions, locally absolutely continuous functions

Received January 26, 2004. (Registered under 5908/2009.)