Abstract. Let sn(T ) denote the nth approximation, isomorphism, Gelfand, Kolmogorov or Bernstein number of the Hardy-type integral operator T given byand mapping a Banach function space E to itself. We investigate some geometrical properties of E for whichunder appropriate conditions on u and v. The constants C 1 , C 2 > 0 depend only on the space E.

Abstract. In the present paper we investigate some geometrical properties of the norms in Banach function spaces. Particularly there is shown that if exponent 1/p(·) belongs to BLO 1/ log then for the norm of corresponding variable exponent Lebesgue space we have the following lower estimate

No abstract

No abstract

No abstract