Littlewood–Paley–Rubio De Francia Inequality for the Two-Parameter Walsh System

Journal of Mathematical Sciences（2022）

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摘要

version of Littlewood–Paley–Rubio de Francia inequality for the two-parameter Walsh system is proved: for any family of disjoint rectangles I_k=I_k^1×I_k^2 in ℤ + × ℤ + and a family of functions f k with Walsh spectrum inside I k the following is true: ‖∑_kf_k‖_L^p≤C_p‖(∑_k|f_k|^2)^1/2‖_L^p,2em 1更多

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walsh

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