On mixed norm holomorphic grand and small spaces

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 $l^q$ sequence. We provide the characterization of functions in such mixed norm spaces and study the boundedness of the holomorphic projection.

Keywords:

• Mixed norm space of holomorphic functions
• grand Lebesgue space
• small Lebesgue space

AMS Subject Classifications:

• 30H20
• 46E30
• 46E15

Acknowledgments

The author confirms that all data generated or analysed during this study are included in this article. This work does not have any conflicts of interest.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by Russian Foundation for Basic Research [20-51-46003-a].