Adyghe Int. Sci. J. Vol. 22, No 3. P. 23-28. ISSN 1726-9946

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DOI: https://doi.org/10.47928/1726-9946-2022-22-3-23-28

MATHEMATICS

MSC 32A10; 32A37

Original Article

On the action of area integral on product domains and bounded functionals in Hardy type spaces

Romi Fayzovich Shamoyan
Ph.D. (Phys. & Math.), Senior Researcher, Bryansk State Technical University, (Bryansk, Russia), ORCID: https://orcid.org/0000-0002-8415-9822, rsham@mail.ru

Abstract.We provide a new maximal theorem for new mixed norm Hardy type spaces and an extention of Hardy-Littlewood theorem to such type mixed norm function spaces related with Area integral on product domains, some new duality results on bounded functionals for such type mixed norm Hardy spaces in product domains will be also provided. We сonsider and discuss also many new function spaces with mixed norm.

Keywords: Bounded linear functionals, Hardy spaces, area integral, product domains, maximal theorem, Hardy-Littlewood type theorem

Acknowledgments: the author are thankful to the anonymous reviewer for his valuable remakes.

For citation. R. F. Shamoyan On the action of area integral on product domains and bounded functionals
in Hardy type spaces. Adyghe Int. Sci. J. 2022. Vol. 22, No. 3. P. 23–28.
DOI: https://doi.org/10.47928/1726-9946-2022-22-3-23-28

The author has read and approved the final version of the manuscript.
Submitted 21.06.2022; approved after reviewing 23.08.2022; accepted for publication 10.10.2022.

© Shamoyan R. F., 2022

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