Weighted holomorphic mixed norm spaces in the unit disc defined in terms of Fourier coefficients

ABSTRACT

Following the ideas of recent research in Karapetyants and Samko [Mixed norm variable exponent Bergman space on the unit disc. Complex Var Elliptic Equ. 2016;61:1090–1106], 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 a general approach for the weighted case. We study the boundedness of the weighted Bergman projection and discuss boundedness and compactness of Toeplitz operators with radial symbols. We also provide a characterization of functions in these spaces.

KEYWORDS:

• Bergman space
• mixed norm
• Toeplitz operators

AMS SUBJECT CLASSIFICATIONS:

• 30H20
• 46E30
• 46E15

Disclosure statement

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

Additional information

Funding

Karapetyants and Smirnova were partially supported by the Russian Foundation for Fundamental Research [grant numbers 20-51-46003-a, 18-01-00094-a].