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Notes on commutator on the variable exponent Lebesgue spaces

Dinghuai Wang (2019)

Czechoslovak Mathematical Journal

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 [ b , T ] is bounded on the variable exponent Lebesgue spaces, then b is a bounded mean oscillation (BMO) function.

Notes on interpolation of Hardy spaces

Quanhua Xu (1992)

Annales de l'institut Fourier

Let H p denote the usual Hardy space of analytic functions on the unit disc ( 0 < p ) . We prove that for every function f H 1 there exists a linear operator T defined on L 1 ( T ) which is simultaneously bounded from L 1 ( T ) to H 1 and from L ( T ) to H such that T ( f ) = f . Consequently, we get the following results ( 1 p 0 , p 1 ) :1) ( H p 0 , H p 1 ) is a Calderon-Mitjagin couple;2) for any interpolation functor F , we have F ( H p 0 , H p 1 ) = H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) , where H ( F ( L p 0 ( T ) , L p 1 ( T ) ) ) denotes the closed subspace of F ( L p 0 ( T ) , L p 1 ( T ) ) of all functions whose Fourier coefficients vanish on negative integers.These results also extend to Hardy...

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