Atomic and Molecular Decomposition of Homogeneous Spaces of Distributions Associated to Non-negative Self-Adjoint Operators
Résumé
We deal with homogeneous Besov and Triebel-Lizorkin spaces 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. The class of almost diagonal operators on the associated sequence spaces is developed and it is shown that this class is an algebra. The boundedness of almost diagonal operators is utilized for establishing smooth molecular and atomic decompositions for the above homogeneous Besov and Triebel-Lizorkin spaces. Spectral multipliers for these spaces are established as well.
Mots clés
Algebra Almost diagonal operators Atomic decomposition Besov spaces Frames Heat kernel Homogeneous spaces Molecular decomposition Spectral multipliers Triebel-Lizorkin spaces Mathematics Subject Classification Primary 58J35 46E35 43A85
Secondary 42B25 42B15 42C15 42C40 Communicated by Dachun Yang
Algebra
Almost diagonal operators
Atomic decomposition
Besov spaces
Frames
Heat kernel
Homogeneous spaces
Molecular decomposition
Spectral multipliers
Triebel-Lizorkin spaces Mathematics Subject Classification Primary 58J35
46E35
43A85
Secondary 42B25
42B15
42C15
42C40 Communicated by Dachun Yang