Dense weakly lacunary subsystems of orthogonal systems and maximal partial sum operator
Dense weakly lacunary subsystems of orthogonal systems and maximal partial sum operator
It is shown that any finite orthogonal system of functions whose norms in $L_p$ are bounded by 1, where $p>2$, has a sufficiently dense subsystem with lacunarity property in the Orlicz space. The norm of the maximal partial sum operator for this subsystem has a better estimate than it is …