The Hardy-Littlewood-Pólya inequality for analytic functions in Hardy-Sobolev spaces

Abstract

For a function of a complex variable analytic in a strip the extremum of the norm of the th derivative is found under a constraint on the -norm of the function and the norm of its th derivative in the metric of the Hardy-Sobolev space. The closely connected problem of the optimal recovery of the th derivative of a function in the Hardy-Sobolev class from the inaccurately given trace of this function on the real axis is also studied. An optimal recovery method is found.