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

Abstract

It is well known that if Hardy-Littlewood maximal operator is bounded in spaceIn the present paper we construct exponent p(•), (1 < p − ≤ p + < ∞), 1/p(•) ∈ BLO 1/ log such that Hardy-Littlewood maximal operator is not bounded in L p(•) [0; 1].