On a Vector-Valued Extension of the Littlewood–Paley–Rubio De Francia Inequality for Walsh Functions

摘要

In the case of trigonometric system, Rubio de Francia proved the one-sided Littlewood–Paley inequality for arbitrary intervals and for the functions in the Lp spaces, 2 ≤ p. Later, Osipov proved a similar inequality for the Walsh system. In this paper, the latter fact is extended to Lp-spaces of functions with values in certain Banach spaces X.