The atomic decomposition of a vector-valued martingale Hardy space is given. A classical inequality of Marcinkiewicz is generalized for UMD lattice valued (bounded) Vilenkin-Fourier series. It is proved that the Vilenkin-Fourier series of f ∈ L P(X) (1 < p < ∞) converges to f in L p(X) norm if and only if X is a UMD space. Moreover, a lacunary sequence of the UMD lattice valued Vilenkin-Fourier series of f ∈ H 1 (X) converges almost everywhere to f in X norm.
|Number of pages||12|
|Publication status||Published - Nov 22 2007|
- Atomic decomposition
- UMD spaces
- Vector-valued Hardy spaces
- Vector-valued Vilenkin-Fourier series
ASJC Scopus subject areas