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math.FA2011★ 1 cited
On the vector-valued Littlewood-Paley-Rubio de Francia inequality
Denis Potapov, Fedor Sukochev, Quanhua Xu
The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LPR_p, 2 \leq p < \infty. The paper shows that every Banach lattice whose 2-concavificatio…
math.FA2010
On operator valued Hardy spaces
Denis Potapov
The note shows that the operator-valued Hardy space $\sH^1$ introduced via Littlewood-Paley -function coincides with the space of $H^1_R(\T, \sL^1)$ of all Bochner integrable op…
math.FA2008
Non- (quantum) differentiable -functions in the spaces with trivial Boyd indices
Denis Potapov, Fyodor Sukochev
If E is a separable symmetric sequence space with trivial Boyd indices and $\cC^E$ is the corresponding ideal of compact operators, then there exists a -function , a self…