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Mat. Zametki, 2018, Volume 104, Issue 3, Pages 439–446 (Mi mz12114)  

On Grand and Small Bergman Spaces

A. N. Karapetyantsab, S. G. Samkoc

a Southern Federal University, Rostov-on-Don
b Don State Technical University, Rostov-on-Don
c Universidade do Algarve

Abstract: Grand and small Bergman spaces of functions holomorphic in the unit disc are introduced. The boundedness of the Bergman projection operator on grand Bergman spaces is proved. The main result consists of estimates for functions in grand and small Bergman spaces near the boundary, which differ from those in the case of the classical Bergman space by a logarithmic multiplier with positive (for grand spaces) or negative (for small spaces) exponent.

Keywords: Bergman space, grand Lebesgue space, small Lebesgue space, Bergman projection, grand Bergman space, small Bergman space, boundary estimates.

Funding Agency Grant Number
Russian Foundation for Basic Research 18-01-00094-a
18-51-05009-Арм-а
This work was supported by the Russian Foundation for Basic Research under grant 18-01-00094-a. The work of the first author was supported in part by the Russian Foundation for Basic Research under grant 18-51-05009-Arm-a.


DOI: https://doi.org/10.4213/mzm12114

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English version:
Mathematical Notes, 2018, 104:3, 431–436

Bibliographic databases:

UDC: 517.53
Received: 25.01.2018

Citation: A. N. Karapetyants, S. G. Samko, “On Grand and Small Bergman Spaces”, Mat. Zametki, 104:3 (2018), 439–446; Math. Notes, 104:3 (2018), 431–436

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