Fractional Integral on Martingale Hardy Spaces With Variable Exponents

Abstract

Abstract In this paper we investigate the boundedness of fractional integral operators on predictable martingale Hardy spaces with variable exponents defined on a probability space. More precisely, let f = (fn)n≥0 be a martingale on probability space (Ω,F, ℙ), and let Iαf, α > 0 be the fractional integral operator associated with f. Under some reasonable assumptions, it is proved that Iαf is bounded on martingale Hardy spaces with variable exponents. Our method is an extension of atomic decomposition theorem to predicable martingale Hardy spaces of variable exponents.