Littlewood–Paley–Rubio de Francia inequality for multi‐parameter Vilenkin systems

Viacheslav Borovitskiy

Mathematische Nachrichten, 2024, vol. 297, issue 3, 1092-1115

Abstract: A version of Littlewood–Paley–Rubio de Francia inequality for bounded multi‐parameter Vilenkin systems is proved: For any family of disjoint sets Ik=Ik1×⋯×IkD⊆Z+D$I_k = I_k^1 \times \cdots \times I_k^D \subseteq {\mathbb {Z}_+^D}$ such that Ikd$I_k^d$ are intervals in Z+$\mathbb {Z}_+$ and a family of functions fk$f_k$ with Vilenkin–Fourier spectrum inside Ik$I_k$ the following holds: ∑kfkLp≤C∑kfk21/2Lp,1

Date: 2024
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