WEAK AND STRONG DYADIC MARTINGALE SPACES WITH VARIABLE EXPONENTS

In this paper, we study the atomic decompositions of weak and strong dyadic martingale spaces with variable exponents. By atomic decompositions, we prove that sublinear operator T is bounded from wHp(·)s to wLp(·); Cesaro operator is bounded from Hp(·) to Lp(·) and from Lp(·) to Lp(·), which generalize the boundedness of operators in constant exponent case.