On the Logarithmic Regularity Conditions for the Variable Exponent Hardy Type Inequality

We discuss a logarithmic regularity condition in a neighborhood of the origin and infinity on the exponent functions q (x) >= p (x) and beta (x) for the variable exponent Hardy inequality parallel to x(beta(.)-1) integral(x)(0) f (t) dt parallel to(Lp(.)(0,l)) <= C parallel to x(beta(.)) f parallel to(Lp(.)(0,l)) to hold.