On mixed norm holomorphic grand and small spaces
Alexey Karapetyants
Abstract
In this paper, we continue the study of new weighted spaces of holomorphic functions on the unit disc with the mixed norm defined in terms of conditions on Fourier coefficients of a function. Here we present the case in which the corresponding conditions are related to grand and small Lebesgues spaces, i.e. the Fourier coefficients as functions of radial variable belong to either grand or small space, and the norms of these coefficients taken in the corresponding space all together form a lq sequence. We provide the characterization of functions in such mixed norm spaces and study the boundedness of the holomorphic projection.
Topics & Concepts
MathematicsHolomorphic functionNorm (philosophy)Pure mathematicsFourier seriesHardy spaceFunction spaceMathematical analysisLawPolitical scienceHolomorphic and Operator TheoryAdvanced Harmonic Analysis ResearchAnalytic and geometric function theory