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This article is cited in 8 scientific papers (total in 8 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/mzm12114https://doi.org/10.4213/mzm12114 https://www.mathnet.ru/eng/mzm/v104/i3/p439
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Abstract page: | 410 | Full-text PDF : | 53 | References: | 45 | First page: | 24 |
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