Some New weak-(\(H_{p}-L_p\)) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series

Abstract

We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some "optimal" weights these new operators are bounded from the martingale Hardy space \(H_{p}(G)\) to the space \(\text{weak-}L_{p}(G)\) , for \(0<p<1/2\). Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.