Note on the strong maximal operator
We obtain the factorization theorem for Hardy space via the variable exponent Lebesgue spaces. As an application, it is proved that if the commutator of Coifman, Rochberg and Weiss is bounded on the variable exponent Lebesgue spaces, then is a bounded mean oscillation (BMO) function.
Let denote the usual Hardy space of analytic functions on the unit disc . We prove that for every function there exists a linear operator defined on which is simultaneously bounded from to and from to such that . Consequently, we get the following results :1) is a Calderon-Mitjagin couple;2) for any interpolation functor , we have , where denotes the closed subspace of of all functions whose Fourier coefficients vanish on negative integers.These results also extend to Hardy...