On the upper and lower estimates of norms in variable exponent spaces

Abstract

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

Hardy-Littlewood Maximal Operator And $BLO^{1/\log}$ Class of Exponents

“…Note that function g is bounded function (some sense analogous of sin(f (x))) which belongs to BLO 1/ log (see [6]). Let denote…”

“…Since g ∈ BLO 1/ log (see [6]), then 1/p(•) ∈ BLO 1/ log . Consequently we have uniformly asymptotic estimation (1.1) for norms χ Q p(•) (see [6]).…”

“…belongs to BLO 1/ log (see [6]). The function f is a classical example of the function from BM O 1/ log (see [9]).…”