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

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

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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:,

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.

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


1. N. Chasova PhD Dissertation. Bryansk, 2001.
2. S. G. Krantz Uniqueness properties of Hardy space functions. The Journal of Geometric Analysis. 2018. Vol. 28. P. 253-264.
3. S. G. Krantz Hardy spaces old and new. In: Explorations in Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Boston.
4. A. Aleksandrov Lecture Notes in Math., 1981.
5. J. Ortega, J. Fabrega Hardy’s inequality and embeddings in holomorphic Triebel-Lizorkin spaces. Illinois J. Math. 1999. Vol. 43, No. 4. P. 733-751.
6. K. Zhu Spaces of Holomorphic Functions in the Unit Ball. Graduate Texts in Mathematics. Vol. 226, Springer-Verlag, New York, 2005.

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