An atomic decomposition of weighted Hardy spaces associated to self-adjoint operators

Hardy Spaces Associated with Non - Negative Self - Adjoint Operators IMI

Maximal and atomic Hardy spaces Hp and H A, 0 < p ≤ 1, are considered in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. It is shown that Hp = H A with equivalent norms.

Hardy Spaces Associated with Non-negative Self-adjoint Operators

Maximal and atomic Hardy spaces Hp and H A, 0 < p ≤ 1, are considered in the setting of a doubling metric measure space in the presence of a non-negative self-adjoint operator whose heat kernel has Gaussian localization and the Markov property. It is shown that Hp = H A with equivalent norms.

On an atomic decomposition in Banach spaces

An atomic decomposition is considered in Banach space.  A method for constructing an atomic decomposition of Banach  space, starting with atomic decomposition of  subspaces  is presented. Some relations between them are established. The proposed method is used in the  study  of the  frame  properties of systems of eigenfunctions and associated functions of discontinuous differential operators.

Generalized composition operators on weighted Hardy spaces

Weighted Composition Operators from Weighted Hardy Spaces to Weighted-type Spaces

The boundedness and compactness of the weighted composition operator from weighted Hardy spaces to weighted-type spaces are studied in this paper.