A Direct Proof of Hardy-Littlewood Maximal Inequality for Operator-valued Functions
We give a direct proof of the operator valued Hardy-Littlewood maximal inequality for $2<p<\infty$.
math.FA↗
arXiv subjects
Zhenchuan Liu
Publications and source records attributed to Zhenchuan Liu.
A Marcinkiewicz Testing Criterion for Schur Multipliers
We prove a Marcinkiewicz testing condition for the boundedness of Schur multipliers on the Schatten $p$-classes. This generalizes a previous work of J. Bourgain for Toeplitz type Schur multipliers. As a corollary, we obtain a new unconditional decomposition for the Schatten $p$-classes ($1<p<\infty$).
math.FA↗
Paley's inequality for nonabelian groups
This article studies Paley's theory for lacunary Fourier series on (nonabelian) discrete groups. The results unify and generalize the work of Rudin for abelian discrete groups and the work of Lust-Piquard and Pisier for operator valued functions, and provide new examples of Paley sequences and $Λ(p)$ sets on free groups.
math.FA↗