A VARIABLE EXPONENT BOUNDEDNESS OF THE STEKLOV OPERATOR

Abstract

In this paper, a sufficiency condition for boundedness of the Steklov operator S(h)f(x) = 1/h integral(x+h)(x) f(t)dt, h > 0 has been proved in variable exponent Lebesgue space L-p(.)(0, infinity). Here an infinite interval (0, infinity) has been considered with a new decay condition on infinity. A finite interval [0, 2 pi] case with a local log- regularity condition has been studied previously in order to be applied on approximation problem.